TSTP Solution File: GEO047-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO047-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 20:34:31 EDT 2022
% Result : Unsatisfiable 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 27
% Syntax : Number of formulae : 50 ( 13 unt; 5 typ; 0 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 263 ( 125 ~; 120 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 1 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 147 ( 136 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $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,
( ~ between(u,v,x)
<=> ~ between(u,v,x) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_between_u_and_x) ).
tff(3,plain,
~ between(u,v,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
tff(8,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,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(12,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(13,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)],[12,11]) ).
tff(14,plain,
~ between(x,v,u),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( between(u,w,x)
<=> between(u,w,x) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
between(u,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_x) ).
tff(17,plain,
between(u,w,x),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,w,x)
| between(x,w,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,w,x)
| between(x,w,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,w,x)
| between(x,w,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,w,x)
| between(x,w,u) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
between(x,w,u),
inference(unit_resolution,[status(thm)],[20,10,17]) ).
tff(22,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(24,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,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(26,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(27,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)],[26,25]) ).
tff(28,plain,
between(w,v,u),
inference(unit_resolution,[status(thm)],[27,10,24]) ).
tff(29,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
<=> ( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
rewrite(
( ( ~ between(U,V,X)
| ~ between(V,W,X)
| between(U,W,X) )
<=> ( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| ~ between(V,W,X)
| between(U,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| ~ between(V,W,X)
| between(U,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).
tff(35,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(x,v,u)
| ~ between(w,v,u)
| ~ between(x,w,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(x,v,u)
| ~ between(w,v,u)
| ~ between(x,w,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ between(x,w,u)
| between(x,v,u)
| ~ between(w,v,u) )
<=> ( between(x,v,u)
| ~ between(w,v,u)
| ~ between(x,w,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(x,w,u)
| between(x,v,u)
| ~ between(w,v,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(x,v,u)
| ~ between(w,v,u)
| ~ between(x,w,u) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(x,w,u)
| between(x,v,u)
| ~ between(w,v,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(x,v,u)
| ~ between(w,v,u)
| ~ between(x,w,u) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| ~ between(x,w,u)
| between(x,v,u)
| ~ between(w,v,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,X)
| between(U,W,X)
| ~ between(V,W,X) )
| between(x,v,u)
| ~ between(w,v,u)
| ~ between(x,w,u) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,38,28,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO047-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.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 04:41:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------