%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM002-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:00:55 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 40
% Syntax : Number of formulae : 81 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 392 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 555 ( 261 ~; 255 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 197 ( 184 !; 0 ?; 197 :)
% Comments :
%------------------------------------------------------------------------------
tff(succeeds_type,type,
succeeds: ( $i * $i ) > $o ).
tff(p8_type,type,
p8: $i ).
tff(p3_type,type,
p3: $i ).
tff(p6_type,type,
p6: $i ).
tff(follows_type,type,
follows: ( $i * $i ) > $o ).
tff(p7_type,type,
p7: $i ).
tff(has_type,type,
has: ( $i * $i ) > $o ).
tff(goto_type,type,
goto: $i > $i ).
tff(loop_type,type,
loop: $i ).
tff(labels_type,type,
labels: ( $i * $i ) > $o ).
tff(1,plain,
( follows(p6,p3)
<=> follows(p6,p3) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
follows(p6,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_3_to_6) ).
tff(3,plain,
follows(p6,p3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Goal_state: $i,Start_state: $i] :
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(5,plain,
( ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [Goal_state: $i,Start_state: $i] :
rewrite(( ( succeeds(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
<=> ( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Goal_state: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [Goal_state: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',direct_success) ).
tff(10,plain,
! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p6,p3)
| succeeds(p6,p3) )
<=> ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p6,p3)
| succeeds(p6,p3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p6,p3)
| succeeds(p6,p3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p6,p3)
| succeeds(p6,p3) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
succeeds(p6,p3),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( ~ succeeds(p3,p3)
<=> ~ succeeds(p3,p3) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
~ succeeds(p3,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_loop_through_p3) ).
tff(20,plain,
~ succeeds(p3,p3),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
^ [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
trans(monotonicity(rewrite(( ( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state) )
<=> ( ~ succeeds(Goal_state,Intermediate_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(Goal_state,Start_state)
| ~ succeeds(Intermediate_state,Start_state) ) )),
rewrite(( ( ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state)
| ~ succeeds(Intermediate_state,Start_state) )
<=> ( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ) )),
( ( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
<=> ( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) )
<=> ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| ~ succeeds(Intermediate_state,Start_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_success) ).
tff(26,plain,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ succeeds(p6,p3)
| ~ succeeds(p3,p6)
| succeeds(p3,p3) )
<=> ( succeeds(p3,p3)
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6)
| succeeds(p3,p3) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6)
| succeeds(p3,p3) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6)
| succeeds(p3,p3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| succeeds(p3,p3)
| ~ succeeds(p6,p3)
| ~ succeeds(p3,p6) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
~ succeeds(p3,p6),
inference(unit_resolution,[status(thm)],[35,29,20,17]) ).
tff(37,plain,
( follows(p8,p7)
<=> follows(p8,p7) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
follows(p8,p7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_7_to_8) ).
tff(39,plain,
follows(p8,p7),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p8,p7)
| succeeds(p8,p7) )
<=> ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p8,p7)
| succeeds(p8,p7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p8,p7)
| succeeds(p8,p7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p8,p7)
| succeeds(p8,p7) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
succeeds(p8,p7),
inference(unit_resolution,[status(thm)],[42,13,39]) ).
tff(44,plain,
( follows(p7,p6)
<=> follows(p7,p6) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
follows(p7,p6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_6_to_7) ).
tff(46,plain,
follows(p7,p6),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p7,p6)
| succeeds(p7,p6) )
<=> ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p7,p6)
| succeeds(p7,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p7,p6)
| succeeds(p7,p6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) )
| ~ follows(p7,p6)
| succeeds(p7,p6) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
succeeds(p7,p6),
inference(unit_resolution,[status(thm)],[49,13,46]) ).
tff(51,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p7,p6)
| ~ succeeds(p8,p7)
| succeeds(p8,p6) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p7,p6)
| ~ succeeds(p8,p7)
| succeeds(p8,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p7,p6)
| ~ succeeds(p8,p7)
| succeeds(p8,p6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p7,p6)
| ~ succeeds(p8,p7)
| succeeds(p8,p6) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
succeeds(p8,p6),
inference(unit_resolution,[status(thm)],[53,29,50,43]) ).
tff(55,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p8,p6)
| ~ succeeds(p3,p8)
| succeeds(p3,p6) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p8,p6)
| ~ succeeds(p3,p8)
| succeeds(p3,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p8,p6)
| ~ succeeds(p3,p8)
| succeeds(p3,p6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) )
| ~ succeeds(p8,p6)
| ~ succeeds(p3,p8)
| succeeds(p3,p6) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ succeeds(p3,p8),
inference(unit_resolution,[status(thm)],[57,29,54,36]) ).
tff(59,plain,
( has(p8,goto(loop))
<=> has(p8,goto(loop)) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
has(p8,goto(loop)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_8) ).
tff(61,plain,
has(p8,goto(loop)),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( labels(loop,p3)
<=> labels(loop,p3) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
labels(loop,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',label_state_3) ).
tff(64,plain,
labels(loop,p3),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
^ [Goal_state: $i,Label: $i,Start_state: $i] :
refl(( ( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
<=> ( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
<=> ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
<=> ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
^ [Goal_state: $i,Label: $i,Start_state: $i] :
trans(monotonicity(rewrite(( ( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label)) )
<=> ( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label)) ) )),
( ( 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) ) )),
rewrite(( ( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
<=> ( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) )),
( ( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
<=> ( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
<=> ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goto_success) ).
tff(71,plain,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) )
<=> ( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( succeeds(p3,p8)
| ~ labels(loop,p3)
| ~ has(p8,goto(loop)) )
<=> ( ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| succeeds(p3,p8)
| ~ labels(loop,p3)
| ~ has(p8,goto(loop)) )
<=> ( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| succeeds(p3,p8)
| ~ labels(loop,p3)
| ~ has(p8,goto(loop)) )
<=> ( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| succeeds(p3,p8)
| ~ labels(loop,p3)
| ~ has(p8,goto(loop)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( succeeds(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ labels(loop,p3)
| succeeds(p3,p8)
| ~ has(p8,goto(loop)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
$false,
inference(unit_resolution,[status(thm)],[80,74,64,61,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : COM002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.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 : Thu Jun 19 12:19:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.22/0.43 % SZS status Unsatisfiable
% 0.22/0.43 % SZS output start Proof
% See solution above
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------