TSTP Solution File: GEO045-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO045-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:30 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 37
% Syntax : Number of formulae : 81 ( 22 unt; 6 typ; 0 def)
% Number of atoms : 342 ( 96 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 431 ( 175 ~; 220 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 2 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 198 ( 181 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(v_type,type,
v: $i ).
tff(w_type,type,
w: $i ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(u_type,type,
u: $i ).
tff(1,plain,
( ( v != w )
<=> ( v != w ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_not_w) ).
tff(3,plain,
v != w,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( between(v,w,x)
<=> between(v,w,x) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_v_and_x) ).
tff(6,plain,
between(v,w,x),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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(11,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)],[10]) ).
tff(12,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
tff(13,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( v = w )
| ~ between(v,w,x)
| ( x = extension(v,w,w,x) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( v = w )
| ~ between(v,w,x)
| ( x = extension(v,w,w,x) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( v = w )
| ~ between(v,w,x)
| ( x = extension(v,w,w,x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( v = w )
| ~ between(v,w,x)
| ( x = extension(v,w,w,x) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
x = extension(v,w,w,x),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
extension(v,w,w,x) = x,
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( between(extension(v,w,w,x),w,v)
<=> between(x,w,v) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( between(x,w,v)
<=> between(extension(v,w,w,x),w,v) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
tff(28,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(v,w,x)
| between(x,w,v) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(v,w,x)
| between(x,w,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(v,w,x)
| between(x,w,v) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(v,w,x)
| between(x,w,v) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
between(x,w,v),
inference(unit_resolution,[status(thm)],[33,30,6]) ).
tff(35,plain,
between(extension(v,w,w,x),w,v),
inference(modus_ponens,[status(thm)],[34,23]) ).
tff(36,plain,
( between(extension(v,w,w,x),v,u)
<=> between(x,v,u) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(37,plain,
( between(x,v,u)
<=> between(extension(v,w,w,x),v,u) ),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ~ between(x,v,u)
<=> ~ between(extension(v,w,w,x),v,u) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ~ between(u,v,x)
<=> ~ between(u,v,x) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
~ between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_between_u_and_x) ).
tff(41,plain,
~ between(u,v,x),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(x,v,u)
| between(u,v,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(x,v,u)
| between(u,v,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(x,v,u)
| between(u,v,x) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(x,v,u)
| between(u,v,x) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ between(x,v,u),
inference(unit_resolution,[status(thm)],[44,30,41]) ).
tff(46,plain,
~ between(extension(v,w,w,x),v,u),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(49,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,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(51,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(52,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)],[51,50]) ).
tff(53,plain,
between(w,v,u),
inference(unit_resolution,[status(thm)],[52,30,49]) ).
tff(54,plain,
( ( w = v )
<=> ( v = w ) ),
inference(commutativity,[status(thm)],]) ).
tff(55,plain,
( ( v = w )
<=> ( w = v ) ),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ( v != w )
<=> ( w != v ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
w != v,
inference(modus_ponens,[status(thm)],[3,56]) ).
tff(58,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
<=> ( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,W,X) )
<=> ( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X) ) )),
( ( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,W,X)
| ( V = W ) )
<=> ( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ) )),
rewrite(
( ( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
<=> ( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ) )),
( ( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,W,X)
| ( V = W ) )
<=> ( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,W,X)
| ( V = W ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,W,X)
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).
tff(64,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
| ( w = v )
| ~ between(extension(v,w,w,x),w,v)
| ~ between(w,v,u)
| between(extension(v,w,w,x),v,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
| ( w = v )
| ~ between(extension(v,w,w,x),w,v)
| ~ between(w,v,u)
| between(extension(v,w,w,x),v,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ between(extension(v,w,w,x),w,v)
| between(extension(v,w,w,x),v,u)
| ~ between(w,v,u)
| ( w = v ) )
<=> ( ( w = v )
| ~ between(extension(v,w,w,x),w,v)
| ~ between(w,v,u)
| between(extension(v,w,w,x),v,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
| ~ between(extension(v,w,w,x),w,v)
| between(extension(v,w,w,x),v,u)
| ~ between(w,v,u)
| ( w = v ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
| ( w = v )
| ~ between(extension(v,w,w,x),w,v)
| ~ between(w,v,u)
| between(extension(v,w,w,x),v,u) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
| ~ between(extension(v,w,w,x),w,v)
| between(extension(v,w,w,x),v,u)
| ~ between(w,v,u)
| ( w = v ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
| ( w = v )
| ~ between(extension(v,w,w,x),w,v)
| ~ between(w,v,u)
| between(extension(v,w,w,x),v,u) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
| ~ between(extension(v,w,w,x),w,v)
| between(extension(v,w,w,x),v,u)
| ~ between(w,v,u)
| ( w = v ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| between(U,W,X)
| ~ between(V,W,X)
| ( V = W ) )
| ( w = v )
| ~ between(extension(v,w,w,x),w,v)
| ~ between(w,v,u)
| between(extension(v,w,w,x),v,u) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ between(extension(v,w,w,x),w,v)
| between(extension(v,w,w,x),v,u) ),
inference(unit_resolution,[status(thm)],[73,67,57,53]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,46,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO045-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 04:59:10 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.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------