TSTP Solution File: GEO053-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO053-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 20:34:33 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 56
% Syntax : Number of formulae : 141 ( 51 unt; 9 typ; 0 def)
% Number of atoms : 402 ( 216 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 429 ( 168 ~; 208 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 4 >; 11 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 359 ( 327 !; 0 ?; 359 :)
% Comments :
%------------------------------------------------------------------------------
tff(w_type,type,
w: $i ).
tff(v_type,type,
v: $i ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(u_type,type,
u: $i ).
tff(insertion_type,type,
insertion: ( $i * $i * $i * $i ) > $i ).
tff(lower_dimension_point_2_type,type,
lower_dimension_point_2: $i ).
tff(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(1,plain,
( ( w = v )
<=> ( v = w ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(4,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i3) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(u,v,w)
| ( v = insertion(u,w,u,v) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(u,v,w)
| ( v = insertion(u,w,u,v) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(u,v,w)
| ( v = insertion(u,w,u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(14,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(u,v,w)
| ( v = insertion(u,w,u,v) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
v = insertion(u,w,u,v),
inference(unit_resolution,[status(thm)],[14,11,4]) ).
tff(16,plain,
insertion(u,w,u,v) = v,
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( ( w = insertion(u,w,u,v) )
<=> ( w = v ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ( w = insertion(u,w,u,v) )
<=> ( v = w ) ),
inference(transitivity,[status(thm)],[17,1]) ).
tff(19,plain,
( ( v = w )
<=> ( w = insertion(u,w,u,v) ) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( v != w )
<=> ( w != insertion(u,w,u,v) ) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ( v != w )
<=> ( v != w ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
v != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_equals_w) ).
tff(23,plain,
v != w,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
w != insertion(u,w,u,v),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
( between(w,insertion(u,w,u,v),u)
<=> between(w,v,u) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(26,plain,
( between(w,v,u)
<=> between(w,insertion(u,w,u,v),u) ),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ between(U,V,W)
| between(W,V,U) )
<=> ( ~ between(U,V,W)
| between(W,V,U) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
tff(31,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
between(w,v,u),
inference(unit_resolution,[status(thm)],[36,33,4]) ).
tff(38,plain,
between(w,insertion(u,w,u,v),u),
inference(modus_ponens,[status(thm)],[37,26]) ).
tff(39,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(
( ( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) )
<=> ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
tff(45,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( w = insertion(u,w,u,v) )
| ~ between(w,insertion(u,w,u,v),u)
| ( u = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( w = insertion(u,w,u,v) )
| ~ between(w,insertion(u,w,u,v),u)
| ( u = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( w = insertion(u,w,u,v) )
| ~ between(w,insertion(u,w,u,v),u)
| ( u = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( w = insertion(u,w,u,v) )
| ~ between(w,insertion(u,w,u,v),u)
| ( u = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( w = insertion(u,w,u,v) )
| ~ between(w,insertion(u,w,u,v),u)
| ( u = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) ) ),
inference(unit_resolution,[status(thm)],[51,48]) ).
tff(53,plain,
u = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),
inference(unit_resolution,[status(thm)],[52,38,24]) ).
tff(54,plain,
extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) = u,
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( between(w,extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
<=> between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
<=> between(w,extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,u,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
^ [V: $i,U: $i] :
refl(
( between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2))
<=> between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2))
<=> ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2))
<=> ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_3) ).
tff(61,plain,
! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2))
| between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2)),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
between(w,extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,u,lower_dimension_point_1,lower_dimension_point_2)),
inference(modus_ponens,[status(thm)],[65,56]) ).
tff(67,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(w,extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(w,extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(w,extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(w,extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ between(w,extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ),
inference(unit_resolution,[status(thm)],[69,33]) ).
tff(71,plain,
between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w),
inference(unit_resolution,[status(thm)],[70,66]) ).
tff(72,plain,
( ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) )
<=> ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(73,plain,
( ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
<=> ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) ) ),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) != u )
<=> ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) != extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( u = extension(w,u,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u ) ),
inference(commutativity,[status(thm)],]) ).
tff(76,plain,
( ( u != extension(w,u,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) != u ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
^ [V: $i,U: $i] :
refl(
( ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
tff(81,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ~ ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
| ( u != extension(w,u,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
u != extension(w,u,lower_dimension_point_1,lower_dimension_point_2),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
extension(w,u,lower_dimension_point_1,lower_dimension_point_2) != u,
inference(modus_ponens,[status(thm)],[85,76]) ).
tff(87,plain,
extension(w,u,lower_dimension_point_1,lower_dimension_point_2) != extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),
inference(modus_ponens,[status(thm)],[86,74]) ).
tff(88,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) )
| ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) )
| ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) )
| ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u) )
| ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) ) ),
inference(unit_resolution,[status(thm)],[90,48,87]) ).
tff(92,plain,
w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w),
inference(unit_resolution,[status(thm)],[91,71]) ).
tff(93,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) = w,
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),
inference(monotonicity,[status(thm)],[54,54]) ).
tff(95,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),extension(w,insertion(u,w,u,v),insertion(u,w,u,v),u),w),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
( equidistant(u,insertion(u,w,u,v),u,w)
<=> equidistant(u,v,u,w) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(97,plain,
( equidistant(u,v,u,w)
<=> equidistant(u,insertion(u,w,u,v),u,w) ),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( equidistant(u,v,u,w)
<=> equidistant(u,v,u,w) ),
inference(rewrite,[status(thm)],]) ).
tff(99,axiom,
equidistant(u,v,u,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u_to_w) ).
tff(100,plain,
equidistant(u,v,u,w),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
equidistant(u,insertion(u,w,u,v),u,w),
inference(modus_ponens,[status(thm)],[100,97]) ).
tff(102,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
<=> ( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
rewrite(
( ( ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) )
| ( U = V ) )
<=> ( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) )
| ( U = V ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
tff(108,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ),
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) )
<=> ( ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ~ equidistant(u,insertion(u,w,u,v),u,w)
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ( extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ),
inference(unit_resolution,[status(thm)],[117,111,101]) ).
tff(119,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),
inference(unit_resolution,[status(thm)],[118,86]) ).
tff(120,plain,
^ [V: $i,W1: $i,U: $i,U1: $i] :
refl(
( ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,axiom,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-3.ax',insertion) ).
tff(124,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
| ( insertion(u,w,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
insertion(u,w,u,insertion(u,w,u,v)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,insertion(u,w,u,v)),
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
insertion(u,w,u,insertion(u,w,u,v)) = insertion(u,w,u,v),
inference(monotonicity,[status(thm)],[16]) ).
tff(130,plain,
insertion(u,w,u,v) = insertion(u,w,u,insertion(u,w,u,v)),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
v = w,
inference(transitivity,[status(thm)],[15,130,128,119,95,93]) ).
tff(132,plain,
$false,
inference(unit_resolution,[status(thm)],[23,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO053-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.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 05:15:36 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.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------