%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT255_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 : n007.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 12:37:20 PM UTC 2026
% Result : Theorem 2.42s 1.24s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 2 prp; 0-4 aty)
% Number of functors : 35 ( 35 usr; 12 con; 0-6 aty)
% Number of variables : 14 ( 12 !; 2 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
arrow_159774573e_indi: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
list: $tType > $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_11,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
arrow_610318064e_Prof: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),bool) ).
tff(func_def_1,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_2,type,
finite_card:
!>[X0: $tType] : ( fun(X0,bool) > nat ) ).
tff(func_def_3,type,
hilbert_inv_into:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * fun(X0,X1) ) > fun(X1,X0) ) ).
tff(func_def_4,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_5,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_6,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_7,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_8,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_9,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_10,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_11,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(product_prod(X0,X1),X2) * X0 * X1 ) > X2 ) ).
tff(func_def_12,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_13,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_14,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_15,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fTrue: bool ).
tff(func_def_18,type,
f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_19,type,
p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_20,type,
c: arrow_411405190le_alt ).
tff(func_def_21,type,
d: arrow_411405190le_alt ).
tff(func_def_22,type,
h: fun(arrow_159774573e_indi,nat) ).
tff(func_def_23,type,
n: nat ).
tff(func_def_24,type,
sK0:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_25,type,
sK1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_26,type,
sK2:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_27,type,
sK3:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_28,type,
sK4: arrow_411405190le_alt ).
tff(func_def_29,type,
sK5: arrow_411405190le_alt ).
tff(func_def_30,type,
sK6: arrow_411405190le_alt ).
tff(func_def_31,type,
sK7: ( arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_411405190le_alt ).
tff(pred_def_1,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
top:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).
tff(pred_def_7,type,
arrow_987702531ctator: ( fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > $o ).
tff(pred_def_8,type,
arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).
tff(pred_def_9,type,
inj_on:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > $o ) ).
tff(pred_def_10,type,
distinct:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_11,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f1,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096c_A_126_061_Ad_096) ).
tff(f2,axiom,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X1 != X0 )
=> ? [X2: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X1,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,X2,nil(arrow_411405190le_alt))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_third__alt) ).
tff(f119,axiom,
! [X0: arrow_411405190le_alt] :
( distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,c,cons(arrow_411405190le_alt,d,cons(arrow_411405190le_alt,X0,nil(arrow_411405190le_alt)))))
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f120,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f121,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f120]) ).
tff(f122,plain,
~ thesis,
inference(flattening,[],[f121]) ).
tff(f123,plain,
! [X0: arrow_411405190le_alt] :
( thesis
| ~ distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,c,cons(arrow_411405190le_alt,d,cons(arrow_411405190le_alt,X0,nil(arrow_411405190le_alt))))) ),
inference(ennf_transformation,[],[f119]) ).
tff(f125,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ? [X2: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X1,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,X2,nil(arrow_411405190le_alt)))))
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f135,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X1,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,sK7(X0,X1),nil(arrow_411405190le_alt)))))
| ( X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f125]) ).
tff(f136,plain,
! [X0: arrow_411405190le_alt] :
( thesis
| ~ distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,c,cons(arrow_411405190le_alt,d,cons(arrow_411405190le_alt,X0,nil(arrow_411405190le_alt))))) ),
inference(cnf_transformation,[],[f123]) ).
tff(f137,plain,
~ thesis,
inference(cnf_transformation,[],[f122]) ).
tff(f155,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X1,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,sK7(X0,X1),nil(arrow_411405190le_alt)))))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f135]) ).
tff(f156,plain,
c != d,
inference(cnf_transformation,[],[f1]) ).
tff(f162,plain,
! [X0: arrow_411405190le_alt] : ~ distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,c,cons(arrow_411405190le_alt,d,cons(arrow_411405190le_alt,X0,nil(arrow_411405190le_alt))))),
inference(forward_subsumption_resolution,[],[f136,f137]) ).
tff(f188,plain,
c = d,
inference(resolution,[],[f155,f162]) ).
tff(f192,plain,
$false,
inference(forward_subsumption_resolution,[],[f188,f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT255_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n007.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 23:59:56 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.42/1.24 % (1908168)Detected formulas, will run a generic FOF schedule.
% 2.42/1.24 % (1908177)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3020780393:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.42/1.24 % (1908177)First to succeed.
% 2.42/1.24 % (1908177)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1908168"
% 2.42/1.24 % (1908173)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=3676916710:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.42/1.24 % (1908175)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=766277683:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.42/1.24 % (1908176)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1415399721:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.42/1.24 % (1908174)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=22208993:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.42/1.24 % (1908176)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.42/1.24 % (1908176)Also succeeded, but the first one will report.
% 2.42/1.24 % (1908178)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2349391691:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.42/1.24 % (1908179)dis-21_1_sil=8000:lcm=predicate:random_seed=2221353092: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)
% 2.42/1.24 % (1908175)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.42/1.24 % (1908178)Also succeeded, but the first one will report.
% 2.42/1.24 % (1908179)Instruction limit reached!
% 2.42/1.24 % (1908179)------------------------------
% 2.42/1.24 % (1908179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.24 % (1908179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.24 % (1908179)CaDiCaL version: 2.1.3
% 2.42/1.24 % (1908179)Termination reason: Instruction limit
% 2.42/1.24 % (1908179)Termination phase: Saturation
% 2.42/1.24 % (1908179)Time elapsed: 0.059 s
% 2.42/1.24 % (1908179)Peak memory usage: 89 MB
% 2.42/1.24 % (1908179)Instructions burned: 130 (million)
% 2.42/1.24 % (1908177)Refutation found. Thanks to Tanya!
% 2.42/1.24 % SZS status Theorem for theBenchmark
% 2.42/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.42/1.25 % (1908177)------------------------------
% 2.42/1.25 % (1908177)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.25 % (1908177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.25 % (1908177)CaDiCaL version: 2.1.3
% 2.42/1.25 % (1908177)Termination reason: Refutation
% 2.42/1.25 % (1908177)Time elapsed: 0.002 s
% 2.42/1.25 % (1908177)Peak memory usage: 88 MB
% 2.42/1.25 % (1908177)Instructions burned: 4 (million)
% 2.42/1.25 % (1908177)------------------------------
% 2.42/1.25 % (1908177)------------------------------
% 2.42/1.25 % (1908168)Success in time 0.276 s
% 2.42/1.25 % Vampire exiting
%------------------------------------------------------------------------------