TSTP Solution File: GEO006-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 20:34:12 EDT 2022
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 55 ( 13 unt; 4 typ; 0 def)
% Number of atoms : 209 ( 64 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 288 ( 134 ~; 135 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 1 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 114 ( 102 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(d_type,type,
d: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( between(a,c,d)
<=> between(a,c,d) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_d) ).
tff(3,plain,
between(a,c,d),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( c != d )
<=> ( c != d ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_d) ).
tff(6,plain,
c != d,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
<=> ( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(
( ( ~ between(U,V,W)
| ~ between(U,W,V)
| ( V = W ) )
<=> ( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ~ between(U,W,V)
| ( V = W ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ~ between(U,W,V)
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
tff(13,plain,
! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
| ( c = d )
| ~ between(a,d,c)
| ~ between(a,c,d) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
| ( c = d )
| ~ between(a,d,c)
| ~ between(a,c,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ( c = d )
| ~ between(a,c,d)
| ~ between(a,d,c) )
<=> ( ( c = d )
| ~ between(a,d,c)
| ~ between(a,c,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
| ( c = d )
| ~ between(a,c,d)
| ~ between(a,d,c) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
| ( c = d )
| ~ between(a,d,c)
| ~ between(a,c,d) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
| ( c = d )
| ~ between(a,c,d)
| ~ between(a,d,c) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
| ( c = d )
| ~ between(a,d,c)
| ~ between(a,c,d) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
| ( c = d )
| ~ between(a,c,d)
| ~ between(a,d,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( V = W )
| ~ between(U,V,W)
| ~ between(U,W,V) )
| ( c = d )
| ~ between(a,d,c)
| ~ between(a,c,d) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ between(a,d,c),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
( ( a != c )
<=> ( a != c ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
tff(26,plain,
a != c,
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) )
<=> ( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(
( ( ~ between(U,V,W)
| ~ between(V,U,W)
| ( U = V ) )
<=> ( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ~ between(V,U,W)
| ( U = V ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ~ between(V,U,W)
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
tff(33,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) )
| ( a = c )
| ~ between(a,c,d)
| ~ between(c,a,d) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) )
| ( a = c )
| ~ between(a,c,d)
| ~ between(c,a,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) )
| ( a = c )
| ~ between(a,c,d)
| ~ between(c,a,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ~ between(V,U,W) )
| ( a = c )
| ~ between(a,c,d)
| ~ between(c,a,d) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ between(c,a,d),
inference(unit_resolution,[status(thm)],[39,36,26,3]) ).
tff(41,plain,
( ( between(c,a,d)
| between(a,d,c) )
<=> ( between(c,a,d)
| between(a,d,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
( between(c,a,d)
| between(a,d,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_not_between_others) ).
tff(43,plain,
( between(c,a,d)
| between(a,d,c) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( between(c,a,d)
| between(a,d,c) ),
inference(modus_ponens,[status(thm)],[43,41]) ).
tff(45,plain,
( between(c,a,d)
| between(a,d,c) ),
inference(modus_ponens,[status(thm)],[44,41]) ).
tff(46,plain,
( between(c,a,d)
| between(a,d,c) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( between(c,a,d)
| between(a,d,c) ),
inference(modus_ponens,[status(thm)],[46,41]) ).
tff(48,plain,
( between(c,a,d)
| between(a,d,c) ),
inference(modus_ponens,[status(thm)],[47,41]) ).
tff(49,plain,
( between(c,a,d)
| between(a,d,c) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( between(c,a,d)
| between(a,d,c) ),
inference(modus_ponens,[status(thm)],[49,41]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.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 04:22:43 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.
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------