TSTP Solution File: MGT045-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT045-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Sun Sep 18 05:22:11 EDT 2022
% Result : Unsatisfiable 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 48 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 270 ( 128 ~; 124 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 102 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
tff(greater_type,type,
greater: ( $i * $i ) > $o ).
tff(external_ties_type,type,
external_ties: ( $i * $i ) > $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(age_type,type,
age: ( $i * $i ) > $i ).
tff(organization_type,type,
organization: $i > $o ).
tff(position_type,type,
position: ( $i * $i ) > $i ).
tff(1,plain,
( greater(age(sk1,sk3),age(sk1,sk2))
<=> greater(age(sk1,sk3),age(sk1,sk2)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
greater(age(sk1,sk3),age(sk1,sk2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_4_34) ).
tff(3,plain,
greater(age(sk1,sk3),age(sk1,sk2)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( organization(sk1)
<=> organization(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
organization(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_4_33) ).
tff(6,plain,
organization(sk1),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
<=> ( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(
( ( ~ organization(A)
| ~ greater(age(A,B),age(A,C))
| greater(external_ties(A,B),external_ties(A,C)) )
<=> ( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ~ greater(age(A,B),age(A,C))
| greater(external_ties(A,B),external_ties(A,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ~ greater(age(A,B),age(A,C))
| greater(external_ties(A,B),external_ties(A,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_8_32) ).
tff(13,plain,
! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1)
| ~ greater(age(sk1,sk3),age(sk1,sk2)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1)
| ~ greater(age(sk1,sk3),age(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1)
| ~ greater(age(sk1,sk3),age(sk1,sk2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1)
| ~ greater(age(sk1,sk3),age(sk1,sk2)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
greater(external_ties(sk1,sk3),external_ties(sk1,sk2)),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( ~ greater(position(sk1,sk3),position(sk1,sk2))
<=> ~ greater(position(sk1,sk3),position(sk1,sk2)) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
~ greater(position(sk1,sk3),position(sk1,sk2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_4_35) ).
tff(23,plain,
~ greater(position(sk1,sk3),position(sk1,sk2)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
<=> ( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(
( ( ~ organization(A)
| ~ greater(external_ties(A,B),external_ties(A,C))
| greater(position(A,B),position(A,C)) )
<=> ( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ~ greater(external_ties(A,B),external_ties(A,C))
| greater(position(A,B),position(A,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ~ greater(external_ties(A,B),external_ties(A,C))
| greater(position(A,B),position(A,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_6_30) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( greater(position(sk1,sk3),position(sk1,sk2))
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1) )
<=> ( greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,33,6,23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MGT045-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Sep 2 03:07:08 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Unsatisfiable
% 0.17/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------