%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n026.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 12:37:10 PM UTC 2026
% Result : Theorem 3.90s 1.57s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 10 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 33 ( 15 ~; 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 : 29 ( 21 !; 8 ?; 29 :)
% 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(f481,plain,
distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK0,cons(arrow_411405190le_alt,sK1,cons(arrow_411405190le_alt,a,nil(arrow_411405190le_alt))))),
inference(forward_demodulation,[],[f203,f368]) ).
tff(f482,plain,
distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK0,cons(arrow_411405190le_alt,a,cons(arrow_411405190le_alt,a,nil(arrow_411405190le_alt))))),
inference(forward_demodulation,[],[f481,f368]) ).
tff(f483,plain,
distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,a,cons(arrow_411405190le_alt,a,cons(arrow_411405190le_alt,a,nil(arrow_411405190le_alt))))),
inference(forward_demodulation,[],[f482,f368]) ).
tff(f484,plain,
$false,
inference(forward_subsumption_resolution,[],[f483,f371]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.12/0.40 % Computer : n026.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 : Mon Sep 28 00:00:12 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.90/1.57 % (3340577)Detected formulas, will run a generic FOF schedule.
% 3.90/1.57 % (3340674)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=2822933291:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.90/1.57 % (3340676)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=2622765136:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.90/1.57 % (3340680)dis-21_1_sil=8000:lcm=predicate:random_seed=4262255929: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)
% 3.90/1.57 % (3340677)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1152703260:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.90/1.57 % (3340679)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3703043184:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.90/1.57 % (3340678)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3704494246:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.90/1.57 % (3340675)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=587330269:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.90/1.57 % (3340678)Refutation not found, incomplete strategy
% 3.90/1.57 % (3340678)------------------------------
% 3.90/1.57 % (3340678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3340677)Refutation not found, incomplete strategy
% 3.90/1.57 % (3340677)------------------------------
% 3.90/1.57 % (3340677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3340678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3340678)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3340677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3340678)Termination reason: Refutation not found, incomplete strategy
% 3.90/1.57 % (3340678)Time elapsed: 0.001 s
% 3.90/1.57 % (3340678)Peak memory usage: 87 MB
% 3.90/1.57 % (3340677)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3340677)Termination reason: Refutation not found, incomplete strategy
% 3.90/1.57 % (3340677)Time elapsed: 0.001 s
% 3.90/1.57 % (3340677)Peak memory usage: 88 MB
% 3.90/1.57 % (3340676)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.90/1.57 % (3340679)First to succeed.
% 3.90/1.57 % (3340679)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3340577"
% 3.90/1.57 % (3340680)Instruction limit reached!
% 3.90/1.57 % (3340680)------------------------------
% 3.90/1.57 % (3340680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3340680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3340680)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3340680)Termination reason: Instruction limit
% 3.90/1.57 % (3340680)Termination phase: Saturation
% 3.90/1.57 % (3340680)Time elapsed: 0.075 s
% 3.90/1.57 % (3340680)Peak memory usage: 89 MB
% 3.90/1.57 % (3340680)Instructions burned: 130 (million)
% 3.90/1.57 % Exception at run slice level
% 3.90/1.57 User error: GNN currently only supports monomorphic FOL.
% 3.90/1.57 % (3340701)lrs+10_1_sil=8000:sp=occurrence:random_seed=1180551996:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.90/1.57 % (3340701)Refutation not found, incomplete strategy
% 3.90/1.57 % (3340701)------------------------------
% 3.90/1.57 % (3340701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3340701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3340701)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3340701)Termination reason: Refutation not found, incomplete strategy
% 3.90/1.57 % (3340701)Time elapsed: 0.001 s
% 3.90/1.57 % (3340701)Peak memory usage: 88 MB
% 3.90/1.57 % (3340678)------------------------------
% 3.90/1.57 % (3340678)------------------------------
% 3.90/1.57 % (3340677)------------------------------
% 3.90/1.57 % (3340677)------------------------------
% 3.90/1.57 % (3340679)Refutation found. Thanks to Tanya!
% 3.90/1.57 % SZS status Theorem for theBenchmark
% 3.90/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 3.90/1.57 % (3340679)------------------------------
% 3.90/1.57 % (3340679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3340679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3340679)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3340679)Termination reason: Refutation
% 3.90/1.57 % (3340679)Time elapsed: 0.011 s
% 3.90/1.57 % (3340679)Peak memory usage: 89 MB
% 3.90/1.57 % (3340679)Instructions burned: 17 (million)
% 3.90/1.57 % (3340679)------------------------------
% 3.90/1.57 % (3340679)------------------------------
% 3.90/1.57 % (3340577)Success in time 0.464 s
% 3.90/1.57 % Vampire exiting
%------------------------------------------------------------------------------