TSTP Solution File: COM002_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM002_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Tue Sep 6 18:05:40 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 54
% Syntax : Number of formulae : 103 ( 26 unt; 10 typ; 0 def)
% Number of atoms : 514 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 712 ( 322 ~; 294 |; 32 &)
% ( 55 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 31 ( 31 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 4 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 245 ( 226 !; 0 ?; 245 :)
% Comments :
%------------------------------------------------------------------------------
tff(succeeds_type,type,
succeeds: ( state * state ) > $o ).
tff(p8_type,type,
p8: state ).
tff(p3_type,type,
p3: state ).
tff(has_type,type,
has: ( state * statement ) > $o ).
tff(goto_type,type,
goto: label > statement ).
tff(loop_type,type,
loop: label ).
tff(labels_type,type,
labels: ( label * state ) > $o ).
tff(p7_type,type,
p7: state ).
tff(p6_type,type,
p6: state ).
tff(follows_type,type,
follows: ( state * state ) > $o ).
tff(1,plain,
( has(p8,goto(loop))
<=> has(p8,goto(loop)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
has(p8,goto(loop)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_8) ).
tff(3,plain,
has(p8,goto(loop)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( labels(loop,p3)
<=> labels(loop,p3) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
labels(loop,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',label_state_3) ).
tff(6,plain,
labels(loop,p3),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [Goal_state: state,Label: label,Start_state: state] :
refl(
( ( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
<=> ( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
<=> ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [Goal_state: state,Label: label,Start_state: state] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
<=> ~ ( ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) )),
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
<=> ~ ~ ( ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) )),
rewrite(
( ~ ~ ( ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
<=> ( ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) )),
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
<=> ( ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) )),
( ( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) )
<=> ( ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state)
| succeeds(Goal_state,Start_state) ) )),
rewrite(
( ( ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state)
| succeeds(Goal_state,Start_state) )
<=> ( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) )),
( ( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) )
<=> ( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [Goal_state: state,Label: label,Start_state: state] :
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) )
<=> ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [Goal_state: state,Label: label,Start_state: state] :
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) )
<=> ! [Goal_state: state,Label: label,Start_state: state] :
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
^ [Goal_state: state,Label: label,Start_state: state] :
rewrite(
( ( ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
=> succeeds(Goal_state,Start_state) )
<=> ( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [Goal_state: state,Label: label,Start_state: state] :
( ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
=> succeeds(Goal_state,Start_state) )
<=> ! [Goal_state: state,Label: label,Start_state: state] :
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,axiom,
! [Goal_state: state,Label: label,Start_state: state] :
( ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
=> succeeds(Goal_state,Start_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goto_success) ).
tff(15,plain,
! [Goal_state: state,Label: label,Start_state: state] :
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Goal_state: state,Label: label,Start_state: state] :
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [Goal_state: state,Label: label,Start_state: state] :
( ~ ( has(Start_state,goto(Label))
& labels(Label,Goal_state) )
| succeeds(Goal_state,Start_state) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ),
inference(modus_ponens,[status(thm)],[18,8]) ).
tff(20,plain,
( ( ~ ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) )
<=> ( ~ ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( succeeds(p3,p8)
| ~ has(p8,goto(loop))
| ~ labels(loop,p3) )
<=> ( ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
| succeeds(p3,p8)
| ~ has(p8,goto(loop))
| ~ labels(loop,p3) )
<=> ( ~ ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
| succeeds(p3,p8)
| ~ has(p8,goto(loop))
| ~ labels(loop,p3) )
<=> ( ~ ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
| succeeds(p3,p8)
| ~ has(p8,goto(loop))
| ~ labels(loop,p3) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [Goal_state: state,Label: label,Start_state: state] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
succeeds(p3,p8),
inference(unit_resolution,[status(thm)],[25,19,6,3]) ).
tff(27,plain,
( follows(p7,p6)
<=> follows(p7,p6) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
follows(p7,p6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_6_to_7) ).
tff(29,plain,
follows(p7,p6),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [Start_state: state,Goal_state: state] :
refl(
( ( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
<=> ( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
<=> ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
<=> ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [Start_state: state,Goal_state: state] :
rewrite(
( ( follows(Goal_state,Start_state)
=> succeeds(Goal_state,Start_state) )
<=> ( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [Start_state: state,Goal_state: state] :
( follows(Goal_state,Start_state)
=> succeeds(Goal_state,Start_state) )
<=> ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [Start_state: state,Goal_state: state] :
( follows(Goal_state,Start_state)
=> succeeds(Goal_state,Start_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',direct_success) ).
tff(36,plain,
! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p7,p6)
| succeeds(p7,p6) )
<=> ( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p7,p6)
| succeeds(p7,p6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p7,p6)
| succeeds(p7,p6) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p7,p6)
| succeeds(p7,p6) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
succeeds(p7,p6),
inference(unit_resolution,[status(thm)],[42,39,29]) ).
tff(44,plain,
( follows(p6,p3)
<=> follows(p6,p3) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
follows(p6,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_3_to_6) ).
tff(46,plain,
follows(p6,p3),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p6,p3)
| succeeds(p6,p3) )
<=> ( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p6,p3)
| succeeds(p6,p3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p6,p3)
| succeeds(p6,p3) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p6,p3)
| succeeds(p6,p3) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
succeeds(p6,p3),
inference(unit_resolution,[status(thm)],[49,39,46]) ).
tff(51,plain,
( ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
<=> ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
^ [Start_state: state,Intermediate_state: state,Goal_state: state] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
<=> ~ ( ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) )),
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
<=> ~ ~ ( ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) )),
rewrite(
( ~ ~ ( ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
<=> ( ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) )),
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
<=> ( ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) )),
( ( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) )
<=> ( ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state)
| succeeds(Goal_state,Start_state) ) )),
rewrite(
( ( ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state)
| succeeds(Goal_state,Start_state) )
<=> ( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) )),
( ( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) )
<=> ( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) )
<=> ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) )
<=> ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [Start_state: state,Intermediate_state: state,Goal_state: state] :
rewrite(
( ( ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
=> succeeds(Goal_state,Start_state) )
<=> ( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
=> succeeds(Goal_state,Start_state) )
<=> ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
=> succeeds(Goal_state,Start_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_success) ).
tff(58,plain,
! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( ~ ( succeeds(Goal_state,Intermediate_state)
& succeeds(Intermediate_state,Start_state) )
| succeeds(Goal_state,Start_state) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ),
inference(modus_ponens,[status(thm)],[61,51]) ).
tff(63,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p6,p3)
| succeeds(p7,p3)
| ~ succeeds(p7,p6) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p6,p3)
| succeeds(p7,p3)
| ~ succeeds(p7,p6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( succeeds(p7,p3)
| ~ succeeds(p7,p6)
| ~ succeeds(p6,p3) )
<=> ( ~ succeeds(p6,p3)
| succeeds(p7,p3)
| ~ succeeds(p7,p6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p7,p3)
| ~ succeeds(p7,p6)
| ~ succeeds(p6,p3) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p6,p3)
| succeeds(p7,p3)
| ~ succeeds(p7,p6) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p7,p3)
| ~ succeeds(p7,p6)
| ~ succeeds(p6,p3) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p6,p3)
| succeeds(p7,p3)
| ~ succeeds(p7,p6) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,plain,
( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p7,p3)
| ~ succeeds(p7,p6)
| ~ succeeds(p6,p3) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p6,p3)
| succeeds(p7,p3)
| ~ succeeds(p7,p6) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
succeeds(p7,p3),
inference(unit_resolution,[status(thm)],[68,62,50,43]) ).
tff(70,plain,
( follows(p8,p7)
<=> follows(p8,p7) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
follows(p8,p7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_7_to_8) ).
tff(72,plain,
follows(p8,p7),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( ( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p8,p7)
| succeeds(p8,p7) )
<=> ( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p8,p7)
| succeeds(p8,p7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p8,p7)
| succeeds(p8,p7) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [Start_state: state,Goal_state: state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p8,p7)
| succeeds(p8,p7) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
succeeds(p8,p7),
inference(unit_resolution,[status(thm)],[75,39,72]) ).
tff(77,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3)
| succeeds(p8,p3) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3)
| succeeds(p8,p3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ( succeeds(p8,p3)
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3) )
<=> ( ~ succeeds(p8,p7)
| ~ succeeds(p7,p3)
| succeeds(p8,p3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p8,p3)
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3)
| succeeds(p8,p3) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p8,p3)
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3)
| succeeds(p8,p3) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p8,p3)
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| ~ succeeds(p8,p7)
| ~ succeeds(p7,p3)
| succeeds(p8,p3) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
succeeds(p8,p3),
inference(unit_resolution,[status(thm)],[82,62,76,69]) ).
tff(84,plain,
( ~ succeeds(p3,p3)
<=> ~ succeeds(p3,p3) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
~ succeeds(p3,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_loop_through_p3) ).
tff(86,plain,
~ succeeds(p3,p3),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p8,p3)
| ~ succeeds(p3,p8) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p8,p3)
| ~ succeeds(p3,p8) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( succeeds(p3,p3)
| ~ succeeds(p3,p8)
| ~ succeeds(p8,p3) )
<=> ( succeeds(p3,p3)
| ~ succeeds(p8,p3)
| ~ succeeds(p3,p8) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p3,p8)
| ~ succeeds(p8,p3) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p8,p3)
| ~ succeeds(p3,p8) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p3,p8)
| ~ succeeds(p8,p3) )
<=> ( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p8,p3)
| ~ succeeds(p3,p8) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p3,p8)
| ~ succeeds(p8,p3) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [Start_state: state,Intermediate_state: state,Goal_state: state] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p8,p3)
| ~ succeeds(p3,p8) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
$false,
inference(unit_resolution,[status(thm)],[92,62,86,83,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM002_1 : TPTP v8.1.0. Released v5.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.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 : Tue Aug 30 13:13:50 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------