%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW619_2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 01:40:32 PM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 13 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 125 ( 36 ~; 13 |; 48 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 230 ( 70 atm; 82 fun; 40 num; 38 var)
% Number of types : 9 ( 7 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 13 usr; 1 prp; 0-7 aty)
% Number of functors : 59 ( 55 usr; 18 con; 0-7 aty)
% Number of variables : 56 ( 42 !; 14 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool1: $tType ).
tff(type_def_8,type,
tuple02: $tType ).
tff(type_def_9,type,
elt4: $tType ).
tff(type_def_10,type,
array_elt2: $tType ).
tff(type_def_11,type,
map_int_elt2: $tType ).
tff(func_def_0,type,
witness1: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool: ty ).
tff(func_def_4,type,
true1: bool1 ).
tff(func_def_5,type,
false1: bool1 ).
tff(func_def_6,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(func_def_7,type,
tuple0: ty ).
tff(func_def_8,type,
tuple03: tuple02 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
map: ( ty * ty ) > ty ).
tff(func_def_13,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(func_def_14,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(func_def_15,type,
const: ( ty * ty * uni ) > uni ).
tff(func_def_16,type,
array: ty > ty ).
tff(func_def_17,type,
mk_array1: ( ty * $int * uni ) > uni ).
tff(func_def_18,type,
length1: ( ty * uni ) > $int ).
tff(func_def_19,type,
elts: ( ty * uni ) > uni ).
tff(func_def_20,type,
get2: ( ty * uni * $int ) > uni ).
tff(func_def_21,type,
t2tb: $int > uni ).
tff(func_def_22,type,
tb2t: uni > $int ).
tff(func_def_23,type,
set2: ( ty * uni * $int * uni ) > uni ).
tff(func_def_24,type,
make1: ( ty * $int * uni ) > uni ).
tff(func_def_25,type,
elt5: ty ).
tff(func_def_26,type,
t2tb7: elt4 > uni ).
tff(func_def_27,type,
tb2t7: uni > elt4 ).
tff(func_def_28,type,
t2tb8: array_elt2 > uni ).
tff(func_def_29,type,
tb2t8: uni > array_elt2 ).
tff(func_def_30,type,
ref: ty > ty ).
tff(func_def_31,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_32,type,
contents: ( ty * uni ) > uni ).
tff(func_def_33,type,
occ1: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_37,type,
abs: $int > $int ).
tff(func_def_39,type,
div: ( $int * $int ) > $int ).
tff(func_def_40,type,
mod: ( $int * $int ) > $int ).
tff(func_def_41,type,
min: ( $int * $int ) > $int ).
tff(func_def_42,type,
max: ( $int * $int ) > $int ).
tff(func_def_43,type,
t2tb9: map_int_elt2 > uni ).
tff(func_def_44,type,
tb2t9: uni > map_int_elt2 ).
tff(func_def_45,type,
sK0: ( array_elt2 * $int * $int ) > $int ).
tff(func_def_46,type,
sK1: ( array_elt2 * $int * $int ) > $int ).
tff(func_def_47,type,
sK2: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_48,type,
sK3: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_49,type,
sK4: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_50,type,
sK5: ( ty * uni * uni * $int * $int ) > uni ).
tff(func_def_51,type,
sK6: ( ty * uni * uni * $int * $int * $int ) > $int ).
tff(func_def_52,type,
sK7: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_53,type,
sK8: ( ty * uni * uni * $int * $int * $int * $int ) > $int ).
tff(func_def_54,type,
sK9: $int ).
tff(func_def_55,type,
sK10: map_int_elt2 ).
tff(func_def_56,type,
sK11: $int ).
tff(func_def_57,type,
sK12: map_int_elt2 ).
tff(func_def_58,type,
sK13: $int ).
tff(func_def_59,type,
sK14: map_int_elt2 ).
tff(func_def_60,type,
sK15: $int ).
tff(pred_def_1,type,
sort1: ( ty * uni ) > $o ).
tff(pred_def_3,type,
le3: ( elt4 * elt4 ) > $o ).
tff(pred_def_4,type,
sorted_sub3: ( array_elt2 * $int * $int ) > $o ).
tff(pred_def_6,type,
sorted3: array_elt2 > $o ).
tff(pred_def_7,type,
permut2: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_8,type,
map_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_9,type,
array_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_10,type,
array_eq: ( ty * uni * uni ) > $o ).
tff(pred_def_11,type,
exchange2: ( ty * uni * uni * $int * $int * $int * $int ) > $o ).
tff(pred_def_12,type,
exchange3: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_13,type,
permut3: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_14,type,
permut_sub1: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_15,type,
permut_all: ( ty * uni * uni ) > $o ).
tff(f98,conjecture,
! [X0: $int,X1: map_int_elt2] :
( $lesseq(0,X0)
=> ! [X2: $int,X3: map_int_elt2] :
( ( $lesseq(0,X2)
& ( X2 = X0 )
& ! [X4: $int] :
( ( $lesseq(0,X4)
& $less(X4,X2) )
=> ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) ) ) )
=> ! [X5: $int,X6: map_int_elt2] :
( ( $lesseq(1,X5)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ! [X7: $int] :
( ( $lesseq(0,$product(X7,X5))
& $less($product(X7,X5),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) ) )
=> ( $less(X5,X0)
=> ! [X7: $int] :
( ( $lesseq(0,$product(X7,X5))
& $less($product(X7,X5),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_bottom_up_mergesort) ).
tff(f99,negated_conjecture,
~ ! [X0: $int,X1: map_int_elt2] :
( $lesseq(0,X0)
=> ! [X2: $int,X3: map_int_elt2] :
( ( $lesseq(0,X2)
& ( X2 = X0 )
& ! [X4: $int] :
( ( $lesseq(0,X4)
& $less(X4,X2) )
=> ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) ) ) )
=> ! [X5: $int,X6: map_int_elt2] :
( ( $lesseq(1,X5)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ! [X7: $int] :
( ( $lesseq(0,$product(X7,X5))
& $less($product(X7,X5),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) ) )
=> ( $less(X5,X0)
=> ! [X7: $int] :
( ( $lesseq(0,$product(X7,X5))
& $less($product(X7,X5),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f98]) ).
tff(f141,plain,
~ ! [X0: $int,X1: map_int_elt2] :
( ~ $less(X0,0)
=> ! [X2: $int,X3: map_int_elt2] :
( ( ~ $less(X2,0)
& ( X2 = X0 )
& ! [X4: $int] :
( ( ~ $less(X4,0)
& $less(X4,X2) )
=> ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) ) ) )
=> ! [X5: $int,X6: map_int_elt2] :
( ( ~ $less(X5,1)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ! [X7: $int] :
( ( ~ $less($product(X7,X5),0)
& $less($product(X7,X5),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) ) )
=> ( $less(X5,X0)
=> ! [X7: $int] :
( ( ~ $less($product(X7,X5),0)
& $less($product(X7,X5),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) ) ) ) ) ),
inference(theory_normalization,[],[f99]) ).
tff(f161,plain,
~ ! [X0: $int,X1: map_int_elt2] :
( ~ $less(X0,0)
=> ! [X2: $int,X3: map_int_elt2] :
( ( ~ $less(X2,0)
& ( X2 = X0 )
& ! [X4: $int] :
( ( ~ $less(X4,0)
& $less(X4,X2) )
=> ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) ) ) )
=> ! [X5: $int,X6: map_int_elt2] :
( ( ~ $less(X5,1)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ! [X7: $int] :
( ( ~ $less($product(X7,X5),0)
& $less($product(X7,X5),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) ) )
=> ( $less(X5,X0)
=> ! [X8: $int] :
( ( ~ $less($product(X8,X5),0)
& $less($product(X8,X5),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5))) ) ) ) ) ),
inference(rectify,[],[f141]) ).
tff(f245,plain,
? [X0: $int,X1: map_int_elt2] :
( ? [X2: $int,X3: map_int_elt2] :
( ? [X5: $int,X6: map_int_elt2] :
( ? [X8: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5)))
& ~ $less($product(X8,X5),0)
& $less($product(X8,X5),X0) )
& $less(X5,X0)
& ~ $less(X5,1)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5)))
| $less($product(X7,X5),0)
| ~ $less($product(X7,X5),X0) ) )
& ~ $less(X2,0)
& ( X2 = X0 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
| $less(X4,0)
| ~ $less(X4,X2) ) )
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f246,plain,
? [X0: $int,X1: map_int_elt2] :
( ? [X2: $int,X3: map_int_elt2] :
( ? [X5: $int,X6: map_int_elt2] :
( ? [X8: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5)))
& ~ $less($product(X8,X5),0)
& $less($product(X8,X5),X0) )
& $less(X5,X0)
& ~ $less(X5,1)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5)))
| $less($product(X7,X5),0)
| ~ $less($product(X7,X5),X0) ) )
& ~ $less(X2,0)
& ( X2 = X0 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
| $less(X4,0)
| ~ $less(X4,X2) ) )
& ~ $less(X0,0) ),
inference(flattening,[],[f245]) ).
tff(f387,plain,
$less($product(sK15,sK13),sK9),
inference(cnf_transformation,[],[f246]) ).
tff(f388,plain,
~ $less($product(sK15,sK13),0),
inference(cnf_transformation,[],[f246]) ).
tff(f389,plain,
~ sorted_sub3(tb2t8(mk_array1(elt5,sK9,t2tb9(sK14))),$product(sK15,sK13),min(sK9,$sum($product(sK15,sK13),sK13))),
inference(cnf_transformation,[],[f246]) ).
tff(f390,plain,
! [X7: $int] :
( ~ $less($product(X7,sK13),sK9)
| $less($product(X7,sK13),0)
| sorted_sub3(tb2t8(mk_array1(elt5,sK9,t2tb9(sK14))),$product(X7,sK13),min(sK9,$sum($product(X7,sK13),sK13))) ),
inference(cnf_transformation,[],[f246]) ).
tff(f395,plain,
sK9 = sK11,
inference(cnf_transformation,[],[f246]) ).
tff(f406,plain,
! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK11,t2tb9(sK14))),$product(X7,sK13),min(sK11,$sum($product(X7,sK13),sK13)))
| $less($product(X7,sK13),0)
| ~ $less($product(X7,sK13),sK11) ),
inference(definition_unfolding,[],[f390,f395,f395,f395]) ).
tff(f407,plain,
~ sorted_sub3(tb2t8(mk_array1(elt5,sK11,t2tb9(sK14))),$product(sK15,sK13),min(sK11,$sum($product(sK15,sK13),sK13))),
inference(definition_unfolding,[],[f389,f395,f395]) ).
tff(f408,plain,
$less($product(sK15,sK13),sK11),
inference(definition_unfolding,[],[f387,f395]) ).
tff(f427,plain,
( $less($product(sK15,sK13),0)
| ~ $less($product(sK15,sK13),sK11) ),
inference(resolution,[],[f406,f407]) ).
tff(f428,plain,
~ $less($product(sK15,sK13),sK11),
inference(forward_subsumption_resolution,[],[f427,f388]) ).
tff(f429,plain,
$false,
inference(forward_subsumption_resolution,[],[f428,f408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW619_2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 14:26:17 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.28 % (2662127)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (2662145)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2888047095:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (2662142)% WARNING: option uhcvi not known.
% 0.20/0.28 % (2662141)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3496398447_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (2662142)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1460466179:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (2662143)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3305660487:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (2662145) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2662127-2662145"...
% 0.20/0.28 % (2662144)dis+10_1_sil=32000:sp=arity:random_seed=284266383:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (2662147)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2931626343:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (2662146)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3975325336:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (2662145)...printing done.
% 0.20/0.28 % (2662145)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (2662145)------------------------------
% 0.20/0.28 % (2662145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2662145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2662145)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2662145)Termination reason: Refutation
% 0.20/0.28 % (2662145)Time elapsed: 0.007 s
% 0.20/0.28 % (2662145)Peak memory usage: 12 MB
% 0.20/0.28 % (2662145)Instructions burned: 22 (million)
% 0.20/0.28 % (2662127)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------