TSTP Solution File: GEO059-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO059-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 20:34:36 EDT 2022
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 73 ( 27 unt; 5 typ; 0 def)
% Number of atoms : 208 ( 18 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 241 ( 112 ~; 101 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 3 >; 7 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 214 ( 194 !; 0 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(v_type,type,
v: $i ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(u_type,type,
u: $i ).
tff(reflection_type,type,
reflection: ( $i * $i ) > $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(
( ( reflection(U,V) = extension(U,V,U,V) )
<=> ( reflection(U,V) = extension(U,V,U,V) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
<=> ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
<=> ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax',reflection) ).
tff(5,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
| ( reflection(u,v) = extension(u,v,u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
reflection(u,v) = extension(u,v,u,v),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
extension(u,v,u,v) = reflection(u,v),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
| ( reflection(reflection(u,v),v) = extension(reflection(u,v),v,reflection(u,v),v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
reflection(reflection(u,v),v) = extension(reflection(u,v),v,reflection(u,v),v),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
extension(reflection(u,v),v,reflection(u,v),v) = reflection(reflection(u,v),v),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( equidistant(v,extension(reflection(u,v),v,reflection(u,v),v),extension(u,v,u,v),v)
<=> equidistant(v,reflection(reflection(u,v),v),reflection(u,v),v) ),
inference(monotonicity,[status(thm)],[13,10]) ).
tff(15,plain,
( equidistant(v,reflection(reflection(u,v),v),reflection(u,v),v)
<=> equidistant(v,extension(reflection(u,v),v,reflection(u,v),v),extension(u,v,u,v),v) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [V: $i,U: $i] :
refl(
( equidistant(V,reflection(U,V),U,V)
<=> equidistant(V,reflection(U,V),U,V) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V)
<=> ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V)
<=> ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_2) ).
tff(20,plain,
! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V)
| equidistant(v,reflection(reflection(u,v),v),reflection(u,v),v) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
equidistant(v,reflection(reflection(u,v),v),reflection(u,v),v),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
equidistant(v,extension(reflection(u,v),v,reflection(u,v),v),extension(u,v,u,v),v),
inference(modus_ponens,[status(thm)],[24,15]) ).
tff(26,plain,
( equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v)
<=> equidistant(reflection(reflection(u,v),v),v,u,v) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(27,plain,
( equidistant(reflection(reflection(u,v),v),v,u,v)
<=> equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ equidistant(reflection(reflection(u,v),v),v,u,v)
<=> ~ equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ~ equidistant(v,u,v,reflection(reflection(u,v),v))
<=> ~ equidistant(v,u,v,reflection(reflection(u,v),v)) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_congruence) ).
tff(31,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
<=> ( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
tff(36,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(reflection(reflection(u,v),v),v,u,v)
| equidistant(v,u,v,reflection(reflection(u,v),v)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(reflection(reflection(u,v),v),v,u,v)
| equidistant(v,u,v,reflection(reflection(u,v),v)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(reflection(reflection(u,v),v),v,u,v)
| equidistant(v,u,v,reflection(reflection(u,v),v)) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(reflection(reflection(u,v),v),v,u,v)
| equidistant(v,u,v,reflection(reflection(u,v),v)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ equidistant(reflection(reflection(u,v),v),v,u,v),
inference(unit_resolution,[status(thm)],[41,38,31]) ).
tff(43,plain,
~ equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v),
inference(modus_ponens,[status(thm)],[42,28]) ).
tff(44,plain,
( equidistant(v,extension(u,v,u,v),u,v)
<=> equidistant(v,reflection(u,v),u,v) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(45,plain,
( equidistant(v,reflection(u,v),u,v)
<=> equidistant(v,extension(u,v,u,v),u,v) ),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [V: $i,U: $i] : equidistant(V,reflection(U,V),U,V)
| equidistant(v,reflection(u,v),u,v) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
equidistant(v,reflection(u,v),u,v),
inference(unit_resolution,[status(thm)],[46,22]) ).
tff(48,plain,
equidistant(v,extension(u,v,u,v),u,v),
inference(modus_ponens,[status(thm)],[47,45]) ).
tff(49,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
refl(
( ( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
<=> ( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
trans(
monotonicity(
rewrite(
( ( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W) )
<=> ( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) )),
( ( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) )
<=> ( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V)
| equidistant(Z,V,V2,W) ) )),
rewrite(
( ( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V)
| equidistant(Z,V,V2,W) )
<=> ( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) )),
( ( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) )
<=> ( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
tff(55,plain,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
| equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v)
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
| equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v)
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
| equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v)
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
| equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v)
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( equidistant(extension(reflection(u,v),v,reflection(u,v),v),v,u,v)
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) ),
inference(unit_resolution,[status(thm)],[61,58]) ).
tff(63,plain,
~ equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v),
inference(unit_resolution,[status(thm)],[62,48,43]) ).
tff(64,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(v,extension(reflection(u,v),v,reflection(u,v),v),extension(u,v,u,v),v)
| equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(v,extension(reflection(u,v),v,reflection(u,v),v),extension(u,v,u,v),v)
| equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(v,extension(reflection(u,v),v,reflection(u,v),v),extension(u,v,u,v),v)
| equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) )
| ~ equidistant(v,extension(reflection(u,v),v,reflection(u,v),v),extension(u,v,u,v),v)
| equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ equidistant(v,extension(reflection(u,v),v,reflection(u,v),v),extension(u,v,u,v),v)
| equidistant(v,extension(u,v,u,v),extension(reflection(u,v),v,reflection(u,v),v),v) ),
inference(unit_resolution,[status(thm)],[66,38]) ).
tff(68,plain,
$false,
inference(unit_resolution,[status(thm)],[67,63,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO059-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 05:06:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------