%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT172_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:37:42 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 35 ( 17 ~; 9 |; 8 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 6 con; 0-5 aty)
% Number of variables : 35 ( 27 !; 8 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
append:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_1,type,
butlast:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_2,type,
dropWhile:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).
tff(func_def_3,type,
hd:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_4,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_5,type,
last:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_6,type,
linorder_insort_key:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
linorder_sort_key:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X0) ) ).
tff(func_def_8,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_9,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_10,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_11,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_12,type,
maps:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).
tff(func_def_13,type,
rev:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_14,type,
rotate1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_15,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_16,type,
takeWhile:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
a: arrow_411405190le_alt ).
tff(func_def_21,type,
sK0: arrow_411405190le_alt ).
tff(func_def_22,type,
sK1: arrow_411405190le_alt ).
tff(func_def_23,type,
sK2: arrow_411405190le_alt ).
tff(func_def_24,type,
sK3: ( arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_411405190le_alt ).
tff(func_def_25,type,
sK4:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_26,type,
sK5:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_27,type,
sK6:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_28,type,
sK7:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_29,type,
sK8:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_30,type,
sK9:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_31,type,
sK10:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_32,type,
sK11:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_33,type,
sK12:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).
tff(func_def_34,type,
sK13:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_35,type,
sK14:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_36,type,
sK15:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_37,type,
sK16:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_38,type,
sK17:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(pred_def_1,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
equal_equal:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_3,type,
distinct:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_4,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_5,type,
null:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(f1,axiom,
? [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X3,cons(arrow_411405190le_alt,X4,cons(arrow_411405190le_alt,X5,nil(arrow_411405190le_alt))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_alt3) ).
tff(f6,axiom,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
<=> ( ( X3 != X2 )
& distinct(X0,cons(X0,X3,X1))
& distinct(X0,cons(X0,X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_distinct__length__2__or__more) ).
tff(f104,conjecture,
? [X0: arrow_411405190le_alt] : ( X0 != a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f105,negated_conjecture,
~ ? [X0: arrow_411405190le_alt] : ( X0 != a ),
inference(negated_conjecture,[status(cth)],[f104]) ).
tff(f106,plain,
? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,X1,cons(arrow_411405190le_alt,X2,nil(arrow_411405190le_alt))))),
inference(rectify,[],[f1]) ).
tff(f146,plain,
! [X0: arrow_411405190le_alt] : ( a = X0 ),
inference(ennf_transformation,[],[f105]) ).
tff(f147,plain,
distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK0,cons(arrow_411405190le_alt,sK1,cons(arrow_411405190le_alt,sK2,nil(arrow_411405190le_alt))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f106]) ).
tff(f151,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( ( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
| ( X2 = X3 )
| ~ distinct(X0,cons(X0,X3,X1))
| ~ distinct(X0,cons(X0,X2,X1)) )
& ( ( ( X3 != X2 )
& distinct(X0,cons(X0,X3,X1))
& distinct(X0,cons(X0,X2,X1)) )
| ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f152,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( ( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
| ( X2 = X3 )
| ~ distinct(X0,cons(X0,X3,X1))
| ~ distinct(X0,cons(X0,X2,X1)) )
& ( ( ( X3 != X2 )
& distinct(X0,cons(X0,X3,X1))
& distinct(X0,cons(X0,X2,X1)) )
| ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ) ),
inference(flattening,[],[f151]) ).
tff(f203,plain,
distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK0,cons(arrow_411405190le_alt,sK1,cons(arrow_411405190le_alt,sK2,nil(arrow_411405190le_alt))))),
inference(cnf_transformation,[],[f147]) ).
tff(f212,plain,
! [X0: $tType,X2: X0,X3: X0,X1: list(X0)] :
( ( X2 != X3 )
| ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ),
inference(cnf_transformation,[],[f152]) ).
tff(f368,plain,
! [X0: arrow_411405190le_alt] : ( a = X0 ),
inference(cnf_transformation,[],[f146]) ).
tff(f371,plain,
! [X0: $tType,X3: X0,X1: list(X0)] : ~ distinct(X0,cons(X0,X3,cons(X0,X3,X1))),
inference(equality_resolution,[],[f212]) ).
tff(f425,plain,
~ distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK0,cons(arrow_411405190le_alt,sK1,cons(arrow_411405190le_alt,sK2,nil(arrow_411405190le_alt))))),
inference(consistent_polarity_flipping,[],[f203]) ).
tff(f430,plain,
! [X0: $tType,X3: X0,X1: list(X0)] : distinct(X0,cons(X0,X3,cons(X0,X3,X1))),
inference(consistent_polarity_flipping,[],[f371]) ).
tff(f453,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ( X0 = X1 ),
inference(superposition,[],[f368,f368]) ).
tff(f535,plain,
! [X0: arrow_411405190le_alt] : ~ distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,sK1,cons(arrow_411405190le_alt,sK2,nil(arrow_411405190le_alt))))),
inference(superposition,[],[f425,f453]) ).
tff(f541,plain,
$false,
inference(resolution,[],[f535,f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT172_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 23:57:17 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.42 Running first-order model finding
% 0.09/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.46 % (302324)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (302335)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=507911003:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (302330)% WARNING: option uhcvi not known.
% 0.15/0.46 % (302329)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2298357679_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (302334)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1962073393:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (302331)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3608364189:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (302330)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2255494961:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (302332)dis+10_1_sil=32000:sp=arity:random_seed=4221758858:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (302335) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-302324-302335"...
% 0.15/0.46 % (302333)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3556253829:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (302335)...printing done.
% 0.15/0.46 % (302335)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (302335)------------------------------
% 0.15/0.46 % (302335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (302335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (302335)CaDiCaL version: 2.1.3
% 0.15/0.46 % (302335)Termination reason: Refutation
% 0.15/0.46 % (302335)Time elapsed: 0.007 s
% 0.15/0.46 % (302335)Peak memory usage: 12 MB
% 0.15/0.46 % (302335)Instructions burned: 21 (million)
% 0.15/0.46 % (302324)Success in time 0.036 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------