TSTP Solution File: GEO077-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO077-4 : TPTP v8.1.0. Released v1.0.0.
% 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 20:34:42 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 66
% Syntax : Number of formulae : 132 ( 39 unt; 9 typ; 0 def)
% Number of atoms : 2494 ( 821 equ)
% Maximal formula atoms : 40 ( 20 avg)
% Number of connectives : 3624 (1425 ~;2059 |; 0 &)
% ( 140 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 172 ( 172 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 336 ( 304 !; 0 ?; 336 :)
% Comments :
%------------------------------------------------------------------------------
tff(on_type,type,
on: ( $i * $i ) > $o ).
tff(line_through_3_points_type,type,
line_through_3_points: ( $i * $i * $i ) > $i ).
tff(point3_type,type,
point3: $i ).
tff(point2_type,type,
point2: $i ).
tff(point1_type,type,
point1: $i ).
tff(a_line_type,type,
a_line: $i ).
tff(collinear_type,type,
collinear: ( $i * $i * $i ) > $o ).
tff(point_type,type,
point: $i > $o ).
tff(line_type,type,
line: $i > $o ).
tff(1,plain,
( collinear(point1,point2,point3)
<=> collinear(point1,point2,point3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
collinear(point1,point2,point3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_points_noncollinear) ).
tff(3,plain,
collinear(point1,point2,point3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( point2 != point3 )
<=> ( point2 != point3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
point2 != point3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_not_point3) ).
tff(6,plain,
point2 != point3,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ( point1 != point3 )
<=> ( point1 != point3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
point1 != point3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point3) ).
tff(9,plain,
point1 != point3,
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( ( point1 != point2 )
<=> ( point1 != point2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
point1 != point2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point2) ).
tff(12,plain,
point1 != point2,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( point(point3)
<=> point(point3) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
point(point3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3) ).
tff(15,plain,
point(point3),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( point(point2)
<=> point(point2) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
point(point2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2) ).
tff(18,plain,
point(point2),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( point(point1)
<=> point(point1) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
point(point1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1) ).
tff(21,plain,
point(point1),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X1,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X1,line_through_3_points(X1,X2,X3)) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X1,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X1,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X1,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X1,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X1,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X1,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X1,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X1,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X1,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X1,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10A) ).
tff(28,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) )
<=> ( ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X1,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point1,line_through_3_points(point1,point2,point3)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
on(point1,line_through_3_points(point1,point2,point3)),
inference(unit_resolution,[status(thm)],[37,31,21,18,15,12,9,6,3]) ).
tff(39,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X2,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X2,line_through_3_points(X1,X2,X3)) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X2,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X2,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X2,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X2,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X2,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X2,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X2,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X2,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X2,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X2,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10B) ).
tff(45,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) )
<=> ( ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X2,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point2,line_through_3_points(point1,point2,point3)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
on(point2,line_through_3_points(point1,point2,point3)),
inference(unit_resolution,[status(thm)],[54,48,21,18,15,12,9,6,3]) ).
tff(56,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| line(line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| line(line_through_3_points(X1,X2,X3)) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| line(line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| line(line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| line(line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| line(line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| line(line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| line(line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| line(line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| line(line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| line(line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| line(line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10D) ).
tff(62,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) )
<=> ( ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| line(line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| line(line_through_3_points(point1,point2,point3)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
line(line_through_3_points(point1,point2,point3)),
inference(unit_resolution,[status(thm)],[71,65,21,18,15,12,9,6,3]) ).
tff(73,plain,
( on(point2,a_line)
<=> on(point2,a_line) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
on(point2,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_on_line) ).
tff(75,plain,
on(point2,a_line),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( on(point1,a_line)
<=> on(point1,a_line) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
on(point1,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_on_line) ).
tff(78,plain,
on(point1,a_line),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( line(a_line)
<=> line(a_line) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
line(a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',line) ).
tff(81,plain,
line(a_line),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
^ [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
refl(
( ( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
<=> ( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
<=> ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
<=> ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3) )
<=> ( ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 ) )
<=> ( ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ( Y3 = Y4 ) ) )),
rewrite(
( ( ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ( Y3 = Y4 ) )
<=> ( ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 ) )
<=> ( ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4) )
<=> ( ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ on(Z1,Y4) ) )),
rewrite(
( ( ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ on(Z1,Y4) )
<=> ( ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4) )
<=> ( ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4) )
<=> ( ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ on(Z2,Y4) ) )),
rewrite(
( ( ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ on(Z2,Y4) )
<=> ( ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4) )
<=> ( ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1) )
<=> ( ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ point(Z1) ) )),
rewrite(
( ( ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ point(Z1) )
<=> ( ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1) )
<=> ( ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1)
| ~ point(Z2) )
<=> ( ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ point(Z2) ) )),
rewrite(
( ( ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ point(Z2) )
<=> ( ~ point(Z2)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1)
| ~ point(Z2) )
<=> ( ~ point(Z2)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1)
| ~ point(Z2)
| ~ line(Y3) )
<=> ( ~ point(Z2)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ line(Y3) ) )),
rewrite(
( ( ~ point(Z2)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ line(Y3) )
<=> ( ~ point(Z2)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1)
| ~ point(Z2)
| ~ line(Y3) )
<=> ( ~ point(Z2)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1)
| ~ point(Z2)
| ~ line(Y3)
| ~ line(Y4) )
<=> ( ~ point(Z2)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ line(Y4) ) )),
rewrite(
( ( ~ point(Z2)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3)
| ~ line(Y4) )
<=> ( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
( ( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1)
| ~ point(Z2)
| ~ line(Y3)
| ~ line(Y4) )
<=> ( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1)
| ~ point(Z2)
| ~ line(Y3)
| ~ line(Y4) )
<=> ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ on(Z1,Y3)
| ( Z1 = Z2 )
| ~ on(Z2,Y3)
| ( Y3 = Y4 )
| ~ on(Z1,Y4)
| ~ on(Z2,Y4)
| ~ point(Z1)
| ~ point(Z2)
| ~ line(Y3)
| ~ line(Y4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1D) ).
tff(88,plain,
! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
| ( point1 = point2 )
| ~ line(a_line)
| ~ point(point1)
| ~ point(point2)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point1,line_through_3_points(point1,point2,point3))
| ~ on(point2,a_line)
| ~ on(point2,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
| ( point1 = point2 )
| ~ line(a_line)
| ~ point(point1)
| ~ point(point2)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point1,line_through_3_points(point1,point2,point3))
| ~ on(point2,a_line)
| ~ on(point2,line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ point(point2)
| ~ line(a_line)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point2,line_through_3_points(point1,point2,point3))
| ( point1 = point2 )
| ~ on(point1,line_through_3_points(point1,point2,point3)) )
<=> ( ( point1 = point2 )
| ~ line(a_line)
| ~ point(point1)
| ~ point(point2)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point1,line_through_3_points(point1,point2,point3))
| ~ on(point2,a_line)
| ~ on(point2,line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ~ ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
| ~ point(point2)
| ~ line(a_line)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point2,line_through_3_points(point1,point2,point3))
| ( point1 = point2 )
| ~ on(point1,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
| ( point1 = point2 )
| ~ line(a_line)
| ~ point(point1)
| ~ point(point2)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point1,line_through_3_points(point1,point2,point3))
| ~ on(point2,a_line)
| ~ on(point2,line_through_3_points(point1,point2,point3)) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
| ~ point(point2)
| ~ line(a_line)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point2,line_through_3_points(point1,point2,point3))
| ( point1 = point2 )
| ~ on(point1,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
| ( point1 = point2 )
| ~ line(a_line)
| ~ point(point1)
| ~ point(point2)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point1,line_through_3_points(point1,point2,point3))
| ~ on(point2,a_line)
| ~ on(point2,line_through_3_points(point1,point2,point3)) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
| ~ point(point2)
| ~ line(a_line)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point2,line_through_3_points(point1,point2,point3))
| ( point1 = point2 )
| ~ on(point1,line_through_3_points(point1,point2,point3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [Y4: $i,Z1: $i,Y3: $i,Z2: $i] :
( ~ point(Z2)
| ~ line(Y4)
| ~ line(Y3)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| ( Y3 = Y4 )
| ~ on(Z2,Y3)
| ( Z1 = Z2 )
| ~ on(Z1,Y3) )
| ( point1 = point2 )
| ~ line(a_line)
| ~ point(point1)
| ~ point(point2)
| ~ line(line_through_3_points(point1,point2,point3))
| ~ on(point1,a_line)
| ( line_through_3_points(point1,point2,point3) = a_line )
| ~ on(point1,line_through_3_points(point1,point2,point3))
| ~ on(point2,a_line)
| ~ on(point2,line_through_3_points(point1,point2,point3)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
line_through_3_points(point1,point2,point3) = a_line,
inference(unit_resolution,[status(thm)],[97,91,21,18,81,78,75,12,72,55,38]) ).
tff(99,plain,
( on(point3,line_through_3_points(point1,point2,point3))
<=> on(point3,a_line) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( on(point3,a_line)
<=> on(point3,line_through_3_points(point1,point2,point3)) ),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ~ on(point3,a_line)
<=> ~ on(point3,line_through_3_points(point1,point2,point3)) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ~ on(point3,a_line)
<=> ~ on(point3,a_line) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
~ on(point3,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3_not_on_line) ).
tff(104,plain,
~ on(point3,a_line),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
~ on(point3,line_through_3_points(point1,point2,point3)),
inference(modus_ponens,[status(thm)],[104,101]) ).
tff(106,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 ) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X3,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X3,line_through_3_points(X1,X2,X3)) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X3,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X3,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X3,line_through_3_points(X1,X2,X3)) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X3,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X3,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X3,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) ) )),
rewrite(
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| on(X3,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ) )),
( ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X3,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X3,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X1 = X2 )
| ( X1 = X3 )
| ( X2 = X3 )
| on(X3,line_through_3_points(X1,X2,X3))
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10C) ).
tff(112,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) )
<=> ( ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ( point2 = point3 )
| ( point1 = point3 )
| ( point1 = point2 )
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ collinear(X1,X2,X3)
| on(X3,line_through_3_points(X1,X2,X3)) )
| ( point1 = point2 )
| ( point1 = point3 )
| ( point2 = point3 )
| ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| ~ collinear(point1,point2,point3)
| on(point3,line_through_3_points(point1,point2,point3)) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
on(point3,line_through_3_points(point1,point2,point3)),
inference(unit_resolution,[status(thm)],[121,115,21,18,15,12,9,6,3]) ).
tff(123,plain,
$false,
inference(unit_resolution,[status(thm)],[122,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO077-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.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 05:31:32 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.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------