TSTP Solution File: GEO019-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO019-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 20:34:19 EDT 2022
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 19
% Syntax : Number of formulae : 33 ( 8 unt; 5 typ; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 102 ( 48 ~; 44 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 1 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 104 ( 96 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(w_type,type,
w: $i ).
tff(u_type,type,
u: $i ).
tff(v_type,type,
v: $i ).
tff(1,plain,
( equidistant(u,v,w,x)
<=> equidistant(u,v,w,x) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
equidistant(u,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
tff(3,plain,
equidistant(u,v,w,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) )
<=> ( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
tff(8,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) )
| ~ equidistant(u,v,w,x)
| equidistant(v,u,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) )
| ~ equidistant(u,v,w,x)
| equidistant(v,u,w,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) )
| ~ equidistant(u,v,w,x)
| equidistant(v,u,w,x) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) )
| ~ equidistant(u,v,w,x)
| equidistant(v,u,w,x) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
equidistant(v,u,w,x),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ equidistant(w,x,v,u)
<=> ~ equidistant(w,x,v,u) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
~ equidistant(w,x,v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetry) ).
tff(17,plain,
~ equidistant(w,x,v,u),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
<=> ( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
tff(22,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(v,u,w,x)
| equidistant(w,x,v,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(v,u,w,x)
| equidistant(w,x,v,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(v,u,w,x)
| equidistant(w,x,v,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(v,u,w,x)
| equidistant(w,x,v,u) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
$false,
inference(unit_resolution,[status(thm)],[27,24,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO019-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.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 04:42:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------