%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW520_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:44 PM UTC 2026
% Result : Theorem 2.64s 1.08s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 17 ~; 11 |; 9 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-6 aty)
% Number of functors : 24 ( 24 usr; 5 con; 0-4 aty)
% Number of variables : 29 ( 23 !; 6 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
hoare_28830079triple: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
pred: $tType > $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_1,type,
complete_Sup_Sup:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_2,type,
suc: nat > nat ).
tff(func_def_3,type,
semiri532925092at_aux:
!>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).
tff(func_def_4,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
powp:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(X0,bool),bool) ) ).
tff(func_def_6,type,
pred1:
!>[X0: $tType] : ( fun(X0,bool) > pred(X0) ) ).
tff(func_def_7,type,
pred_case:
!>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,bool),X1) * pred(X0) ) > X1 ) ).
tff(func_def_8,type,
pred_rec:
!>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,bool),X1) * pred(X0) ) > X1 ) ).
tff(func_def_9,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_10,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_11,type,
fFalse: bool ).
tff(func_def_12,type,
fTrue: bool ).
tff(func_def_13,type,
ga: fun(hoare_28830079triple(a),bool) ).
tff(func_def_14,type,
sK0: nat ).
tff(func_def_15,type,
sK1: hoare_28830079triple(a) ).
tff(func_def_16,type,
sK2:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_17,type,
sK3:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_18,type,
sK4:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_19,type,
sK5:
!>[X0: $tType] : ( ( nat * fun(hoare_28830079triple(X0),bool) ) > hoare_28830079triple(X0) ) ).
tff(func_def_20,type,
sK6:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(pred_def_1,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
comple187826305attice:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
hoare_592965047valids:
!>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).
tff(pred_def_9,type,
hoare_1633586161_valid:
!>[X0: $tType] : ( ( nat * hoare_28830079triple(X0) ) > $o ) ).
tff(pred_def_10,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_12,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(f2,axiom,
! [X0: $tType,X1: fun(X0,bool)] :
( ! [X2: X0] : ~ member(X0,X2,X1)
<=> ( X1 = bot_bot(fun(X0,bool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_all__not__in__conv) ).
tff(f126,conjecture,
! [X0: nat] :
( ? [X1: hoare_28830079triple(a)] :
( member(hoare_28830079triple(a),X1,ga)
& ~ hoare_1633586161_valid(a,X0,X1) )
| ! [X2: hoare_28830079triple(a)] :
( member(hoare_28830079triple(a),X2,bot_bot(fun(hoare_28830079triple(a),bool)))
=> hoare_1633586161_valid(a,X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f127,negated_conjecture,
~ ! [X0: nat] :
( ? [X1: hoare_28830079triple(a)] :
( member(hoare_28830079triple(a),X1,ga)
& ~ hoare_1633586161_valid(a,X0,X1) )
| ! [X2: hoare_28830079triple(a)] :
( member(hoare_28830079triple(a),X2,bot_bot(fun(hoare_28830079triple(a),bool)))
=> hoare_1633586161_valid(a,X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f126]) ).
tff(f128,plain,
? [X0: nat] :
( ! [X1: hoare_28830079triple(a)] :
( ~ member(hoare_28830079triple(a),X1,ga)
| hoare_1633586161_valid(a,X0,X1) )
& ? [X2: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X0,X2)
& member(hoare_28830079triple(a),X2,bot_bot(fun(hoare_28830079triple(a),bool))) ) ),
inference(ennf_transformation,[],[f127]) ).
tff(f144,plain,
( ! [X1: hoare_28830079triple(a)] :
( ~ member(hoare_28830079triple(a),X1,ga)
| hoare_1633586161_valid(a,sK0,X1) )
& ~ hoare_1633586161_valid(a,sK0,sK1)
& member(hoare_28830079triple(a),sK1,bot_bot(fun(hoare_28830079triple(a),bool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f128]) ).
tff(f150,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ! [X2: X0] : ~ member(X0,X2,X1)
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( X1 = bot_bot(fun(X0,bool)) )
| ? [X2: X0] : member(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
tff(f151,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ! [X2: X0] : ~ member(X0,X2,X1)
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( X1 = bot_bot(fun(X0,bool)) )
| ? [X3: X0] : member(X0,X3,X1) ) ),
inference(rectify,[],[f150]) ).
tff(f152,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ! [X2: X0] : ~ member(X0,X2,X1)
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( X1 = bot_bot(fun(X0,bool)) )
| member(X0,sK4(X0,X1),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1))],[f151]) ).
tff(f156,plain,
member(hoare_28830079triple(a),sK1,bot_bot(fun(hoare_28830079triple(a),bool))),
inference(cnf_transformation,[],[f144]) ).
tff(f169,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ member(X0,X2,X1)
| ( bot_bot(fun(X0,bool)) != X1 ) ),
inference(cnf_transformation,[],[f152]) ).
tff(f184,plain,
! [X0: $tType,X2: X0] : ~ member(X0,X2,bot_bot(fun(X0,bool))),
inference(equality_resolution,[],[f169]) ).
tff(f185,plain,
$false,
inference(forward_subsumption_resolution,[],[f156,f184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW520_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:17:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.64/1.08 % (4022412)Detected formulas, will run a generic FOF schedule.
% 2.64/1.08 % (4022420)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1712288515:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.08 % (4022420)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.64/1.08 % (4022420)First to succeed.
% 2.64/1.08 % (4022420)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4022412"
% 2.64/1.08 % (4022423)dis-21_1_sil=8000:lcm=predicate:random_seed=3196262062:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.64/1.08 % (4022419)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2730379834:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.08 % (4022417)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4291734368:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.08 % (4022422)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1616523545:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.08 % (4022421)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3777028702:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.08 % (4022418)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4156934427:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.08 % (4022421)Also succeeded, but the first one will report.
% 2.64/1.08 % (4022419)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.64/1.08 % (4022423)Also succeeded, but the first one will report.
% 2.64/1.08 % (4022422)Also succeeded, but the first one will report.
% 2.64/1.08 % (4022420)Refutation found. Thanks to Tanya!
% 2.64/1.08 % SZS status Theorem for theBenchmark
% 2.64/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.08 % (4022420)------------------------------
% 2.64/1.08 % (4022420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.08 % (4022420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.08 % (4022420)CaDiCaL version: 2.1.3
% 2.64/1.08 % (4022420)Termination reason: Refutation
% 2.64/1.08 % (4022420)Time elapsed: 0.002 s
% 2.64/1.08 % (4022420)Peak memory usage: 88 MB
% 2.64/1.08 % (4022420)Instructions burned: 2 (million)
% 2.64/1.08 % (4022420)------------------------------
% 2.64/1.08 % (4022420)------------------------------
% 2.64/1.08 % (4022412)Success in time 0.301 s
% 2.64/1.08 % Vampire exiting
%------------------------------------------------------------------------------