%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM002-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 39
% Syntax : Number of formulae : 79 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 350 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 502 ( 236 ~; 234 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 192 ( 178 !; 0 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
tff(fails_type,type,
fails: ( $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/sandbox/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(( ( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
<=> ( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',direct_success) ).
tff(8,plain,
! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p6,p3)
| ~ follows(p6,p3) )
<=> ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p6,p3)
| ~ follows(p6,p3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p6,p3)
| ~ follows(p6,p3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p6,p3)
| ~ follows(p6,p3) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ fails(p6,p3),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( fails(p3,p3)
<=> fails(p3,p3) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
fails(p3,p3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_loop_through_p3) ).
tff(17,plain,
fails(p3,p3),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
refl(( ( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
<=> ( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
<=> ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
rewrite(( ( ~ fails(Goal_state,Start_state)
| fails(Goal_state,Intermediate_state)
| fails(Intermediate_state,Start_state) )
<=> ( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| fails(Goal_state,Intermediate_state)
| fails(Intermediate_state,Start_state) )
<=> ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| fails(Goal_state,Intermediate_state)
| fails(Intermediate_state,Start_state) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_success) ).
tff(24,plain,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| ~ fails(p3,p3)
| fails(p6,p3)
| fails(p3,p6) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| ~ fails(p3,p3)
| fails(p6,p3)
| fails(p3,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( fails(p6,p3)
| fails(p3,p6)
| ~ fails(p3,p3) )
<=> ( ~ fails(p3,p3)
| fails(p6,p3)
| fails(p3,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p6,p3)
| fails(p3,p6)
| ~ fails(p3,p3) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| ~ fails(p3,p3)
| fails(p6,p3)
| fails(p3,p6) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p6,p3)
| fails(p3,p6)
| ~ fails(p3,p3) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| ~ fails(p3,p3)
| fails(p6,p3)
| fails(p3,p6) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p6,p3)
| fails(p3,p6)
| ~ fails(p3,p3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| ~ fails(p3,p3)
| fails(p6,p3)
| fails(p3,p6) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
fails(p3,p6),
inference(unit_resolution,[status(thm)],[33,27,17,14]) ).
tff(35,plain,
( follows(p8,p7)
<=> follows(p8,p7) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
follows(p8,p7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transition_7_to_8) ).
tff(37,plain,
follows(p8,p7),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p8,p7)
| ~ follows(p8,p7) )
<=> ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p8,p7)
| ~ follows(p8,p7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p8,p7)
| ~ follows(p8,p7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p8,p7)
| ~ follows(p8,p7) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
~ fails(p8,p7),
inference(unit_resolution,[status(thm)],[40,10,37]) ).
tff(42,plain,
( follows(p7,p6)
<=> follows(p7,p6) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
follows(p7,p6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transition_6_to_7) ).
tff(44,plain,
follows(p7,p6),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p7,p6)
| ~ follows(p7,p6) )
<=> ( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p7,p6)
| ~ follows(p7,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p7,p6)
| ~ follows(p7,p6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Goal_state: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ follows(Goal_state,Start_state) )
| ~ fails(p7,p6)
| ~ follows(p7,p6) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ fails(p7,p6),
inference(unit_resolution,[status(thm)],[47,10,44]) ).
tff(49,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p7,p6)
| fails(p8,p7)
| ~ fails(p8,p6) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p7,p6)
| fails(p8,p7)
| ~ fails(p8,p6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p7,p6)
| fails(p8,p7)
| ~ fails(p8,p6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p7,p6)
| fails(p8,p7)
| ~ fails(p8,p6) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
~ fails(p8,p6),
inference(unit_resolution,[status(thm)],[51,27,48,41]) ).
tff(53,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p8,p6)
| ~ fails(p3,p6)
| fails(p3,p8) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p8,p6)
| ~ fails(p3,p6)
| fails(p3,p8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( fails(p8,p6)
| fails(p3,p8)
| ~ fails(p3,p6) )
<=> ( fails(p8,p6)
| ~ fails(p3,p6)
| fails(p3,p8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p8,p6)
| fails(p3,p8)
| ~ fails(p3,p6) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p8,p6)
| ~ fails(p3,p6)
| fails(p3,p8) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p8,p6)
| fails(p3,p8)
| ~ fails(p3,p6) )
<=> ( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p8,p6)
| ~ fails(p3,p6)
| fails(p3,p8) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p8,p6)
| fails(p3,p8)
| ~ fails(p3,p6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [Goal_state: $i,Intermediate_state: $i,Start_state: $i] :
( fails(Intermediate_state,Start_state)
| fails(Goal_state,Intermediate_state)
| ~ fails(Goal_state,Start_state) )
| fails(p8,p6)
| ~ fails(p3,p6)
| fails(p3,p8) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
fails(p3,p8),
inference(unit_resolution,[status(thm)],[58,27,52,34]) ).
tff(60,plain,
( has(p8,goto(loop))
<=> has(p8,goto(loop)) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
has(p8,goto(loop)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',state_8) ).
tff(62,plain,
has(p8,goto(loop)),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( labels(loop,p3)
<=> labels(loop,p3) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
labels(loop,p3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',label_state_3) ).
tff(65,plain,
labels(loop,p3),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
^ [Goal_state: $i,Label: $i,Start_state: $i] :
refl(( ( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
<=> ( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
<=> ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
<=> ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
^ [Goal_state: $i,Label: $i,Start_state: $i] :
rewrite(( ( ~ fails(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
<=> ( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) )
<=> ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ has(Start_state,goto(Label))
| ~ labels(Label,Goal_state) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goto_success) ).
tff(72,plain,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ fails(p3,p8)
| ~ labels(loop,p3)
| ~ has(p8,goto(loop)) )
<=> ( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ fails(p3,p8)
| ~ labels(loop,p3)
| ~ has(p8,goto(loop)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ fails(p3,p8)
| ~ labels(loop,p3)
| ~ has(p8,goto(loop)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [Goal_state: $i,Label: $i,Start_state: $i] :
( ~ fails(Goal_state,Start_state)
| ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label)) )
| ~ fails(p3,p8)
| ~ labels(loop,p3)
| ~ has(p8,goto(loop)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,75,65,62,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM002-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 12:24:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------