TSTP Solution File: GEO016-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO016-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 20:34:18 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 34 ( 13 unt; 5 typ; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 143 ( 68 ~; 61 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 1 >; 3 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 122 ( 108 !; 0 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(u_type,type,
u: $i ).
tff(v_type,type,
v: $i ).
tff(x_type,type,
x: $i ).
tff(w_type,type,
w: $i ).
tff(1,plain,
( ~ equidistant(v,u,w,x)
<=> ~ equidistant(v,u,w,x) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ equidistant(v,u,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetry) ).
tff(3,plain,
~ equidistant(v,u,w,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( equidistant(u,v,w,x)
<=> equidistant(u,v,w,x) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
equidistant(u,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
tff(6,plain,
equidistant(u,v,w,x),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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(11,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)],[10]) ).
tff(12,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(13,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)],[12,11]) ).
tff(14,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)],[13,9]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,8]) ).
tff(17,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(v,u,w,x)
| ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,v,u) )
<=> ( ~ ! [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(v,u,w,x)
| ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,v,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,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(v,u,w,x)
| ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,v,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,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(v,u,w,x)
| ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,v,u) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ equidistant(u,v,v,u),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(
( equidistant(X,Y,Y,X)
<=> equidistant(X,Y,Y,X) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : equidistant(X,Y,Y,X)
<=> ! [Y: $i,X: $i] : equidistant(X,Y,Y,X) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : equidistant(X,Y,Y,X)
<=> ! [Y: $i,X: $i] : equidistant(X,Y,Y,X) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [Y: $i,X: $i] : equidistant(X,Y,Y,X),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
tff(25,plain,
! [Y: $i,X: $i] : equidistant(X,Y,Y,X),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : equidistant(X,Y,Y,X),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : equidistant(X,Y,Y,X),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : equidistant(X,Y,Y,X)
| equidistant(u,v,v,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,27,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO016-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 05:03:47 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------