%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW530_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 : n008.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 01:30:45 PM UTC 2026
% Result : Theorem 4.94s 1.67s
% Output : Refutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 105 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 99 ( 45 ~; 44 |; 1 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 4 prp; 0-4 aty)
% Number of functors : 24 ( 24 usr; 5 con; 0-5 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
b: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
huffma1450048681e_tree: $tType > $tType ).
tff(type_def_9,type,
int: $tType ).
tff(type_def_10,type,
list: $tType > $tType ).
tff(type_def_11,type,
nat: $tType ).
tff(type_def_12,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
huffma410068972_depth:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_2,type,
huffma945805758height:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_3,type,
huffma632063779ight_F:
!>[X0: $tType] : ( list(huffma1450048681e_tree(X0)) > nat ) ).
tff(func_def_4,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_5,type,
nat1: int > nat ).
tff(func_def_6,type,
ring_1_of_int:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
linorder_insort_key:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 * list(X0) ) > list(X0) ) ).
tff(func_def_8,type,
linorder_sort_key:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X0) ) ).
tff(func_def_9,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > 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,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_13,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_14,type,
ord_max:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
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,
a1: a ).
tff(func_def_19,type,
t_1: huffma1450048681e_tree(b) ).
tff(func_def_20,type,
t_2: huffma1450048681e_tree(a) ).
tff(pred_def_1,type,
ring_1:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
null:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_12,type,
nat_tr1645093318rphism:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > $o ) ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
order_strict_mono:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > $o ) ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(pred_def_17,type,
sP0: nat > $o ).
tff(f2,axiom,
! [X0: $tType,X1: X0,X2: huffma1450048681e_tree(X0)] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_depth__le__height) ).
tff(f9,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
<=> ( ord_max(X0,X2,X1) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_min__max_Ole__iff__sup) ).
tff(f14,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
=> ( ord_max(X0,X1,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_min__max_Osup__absorb1) ).
tff(f48,axiom,
! [X0: nat,X1: nat] :
( ord_less_eq(nat,X1,X0)
| ord_less_eq(nat,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_nat__le__linear) ).
tff(f117,axiom,
linorder(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
tff(f130,axiom,
huffma410068972_depth(a,t_2,a1) = ord_max(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f131,axiom,
( ( huffma410068972_depth(a,t_2,a1) = huffma945805758height(a,t_2) )
=> ( ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
=> p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f132,conjecture,
p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f133,negated_conjecture,
~ p,
inference(negated_conjecture,[status(cth)],[f132]) ).
tff(f134,plain,
~ p,
inference(flattening,[],[f133]) ).
tff(f136,plain,
( p
| ~ ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
| ( huffma410068972_depth(a,t_2,a1) != huffma945805758height(a,t_2) ) ),
inference(ennf_transformation,[],[f131]) ).
tff(f137,plain,
( p
| ~ ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
| ( huffma410068972_depth(a,t_2,a1) != huffma945805758height(a,t_2) ) ),
inference(flattening,[],[f136]) ).
tff(f159,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_max(X0,X1,X2) = X1 )
| ~ ord_less_eq(X0,X2,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f164,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
<=> ( ord_max(X0,X2,X1) = X1 ) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f172,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less_eq(X0,X2,X1)
| ( ord_max(X0,X2,X1) != X1 ) )
& ( ( ord_max(X0,X2,X1) = X1 )
| ~ ord_less_eq(X0,X2,X1) ) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f164]) ).
tff(f175,plain,
huffma410068972_depth(a,t_2,a1) = ord_max(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2)),
inference(cnf_transformation,[],[f130]) ).
tff(f176,plain,
( p
| ~ ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
| ( huffma410068972_depth(a,t_2,a1) != huffma945805758height(a,t_2) ) ),
inference(cnf_transformation,[],[f137]) ).
tff(f177,plain,
~ p,
inference(cnf_transformation,[],[f134]) ).
tff(f178,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2)),
inference(cnf_transformation,[],[f2]) ).
tff(f181,plain,
linorder(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f184,plain,
! [X0: nat,X1: nat] :
( ord_less_eq(nat,X1,X0)
| ord_less_eq(nat,X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f200,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( ord_max(X0,X1,X2) = X1 )
| ~ ord_less_eq(X0,X2,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f159]) ).
tff(f207,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( ord_max(X0,X2,X1) = X1 )
| ~ ord_less_eq(X0,X2,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f172]) ).
tff(f216,definition,
~ sP0(huffma410068972_depth(a,t_2,a1)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
tff(f217,plain,
( p
| ~ ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
| sP0(huffma945805758height(a,t_2)) ),
inference(inequality_splitting,[],[f176,f216]) ).
tff(f219,plain,
( ~ ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
| sP0(huffma945805758height(a,t_2)) ),
inference(forward_subsumption_resolution,[],[f217,f177]) ).
tff(f221,definition,
( spl1_1
<=> sP0(huffma945805758height(a,t_2)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f223,plain,
( sP0(huffma945805758height(a,t_2))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f221]) ).
tff(f225,definition,
( spl1_2
<=> ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f226,plain,
( ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f225]) ).
tff(f227,plain,
( ~ ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
| spl1_2 ),
inference(avatar_component_clause,[],[f225]) ).
tff(f228,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f219,f225,f221]) ).
tff(f229,plain,
( ord_less_eq(nat,huffma945805758height(a,t_2),huffma945805758height(b,t_1))
| spl1_2 ),
inference(resolution,[],[f227,f184]) ).
tff(f270,plain,
( ( huffma410068972_depth(a,t_2,a1) = huffma945805758height(b,t_1) )
| ~ ord_less_eq(nat,huffma945805758height(a,t_2),huffma945805758height(b,t_1))
| ~ linorder(nat) ),
inference(superposition,[],[f200,f175]) ).
tff(f277,plain,
( ( huffma410068972_depth(a,t_2,a1) = huffma945805758height(a,t_2) )
| ~ ord_less_eq(nat,huffma945805758height(b,t_1),huffma945805758height(a,t_2))
| ~ linorder(nat) ),
inference(superposition,[],[f207,f175]) ).
tff(f299,plain,
( ( huffma410068972_depth(a,t_2,a1) = huffma945805758height(b,t_1) )
| ~ linorder(nat)
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f270,f229]) ).
tff(f323,plain,
( ( huffma410068972_depth(a,t_2,a1) = huffma945805758height(b,t_1) )
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f299,f181]) ).
tff(f330,plain,
( ~ ord_less_eq(nat,huffma410068972_depth(a,t_2,a1),huffma945805758height(a,t_2))
| spl1_2 ),
inference(superposition,[],[f227,f323]) ).
tff(f336,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f330,f178]) ).
tff(f337,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f336]) ).
tff(f339,plain,
( ( huffma410068972_depth(a,t_2,a1) = huffma945805758height(a,t_2) )
| ~ linorder(nat)
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f277,f226]) ).
tff(f347,plain,
( ( huffma410068972_depth(a,t_2,a1) = huffma945805758height(a,t_2) )
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f339,f181]) ).
tff(f363,plain,
( ~ sP0(huffma945805758height(a,t_2))
| ~ spl1_2 ),
inference(superposition,[],[f216,f347]) ).
tff(f366,plain,
( $false
| ~ spl1_1
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f363,f223]) ).
tff(f367,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_contradiction_clause,[],[f366]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f228]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f337]) ).
cnf(s5,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f367]) ).
cnf(s6,plain,
~ spl1_1,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s2,s6]) ).
tff(f368,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW530_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.27 % Computer : n008.cluster.edu
% 0.23/0.27 % Model : x86_64 x86_64
% 0.23/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.27 % Memory : 8046.5625MB
% 0.23/0.27 % OS : Linux 6.8.0-71-generic
% 0.23/0.27 % CPULimit : 300
% 0.23/0.27 % WCLimit : 300
% 0.23/0.27 % DateTime : Mon Sep 28 14:18:09 UTC 2026
% 0.23/0.27 % CPUTime :
% 0.23/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.31 Running first-order theorem proving
% 0.23/0.31 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
% 4.94/1.67 % (2278062)Detected formulas, will run a generic FOF schedule.
% 4.94/1.67 % (2278071)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=3567346667:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.94/1.67 % (2278074)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1886817472:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.94/1.67 % (2278072)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=4278542126:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.94/1.67 % (2278073)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=1844993936:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.94/1.67 % (2278074)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.94/1.67 % (2278073)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.94/1.67 % (2278075)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4192379574:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.94/1.67 % (2278077)dis-21_1_sil=8000:lcm=predicate:random_seed=2259773662: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)
% 4.94/1.67 % (2278076)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3148144851:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.94/1.67 % (2278074)First to succeed.
% 4.94/1.67 % (2278074)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2278062"
% 4.94/1.67 % (2278075)Also succeeded, but the first one will report.
% 4.94/1.67 % (2278076)Also succeeded, but the first one will report.
% 4.94/1.67 % (2278077)Instruction limit reached!
% 4.94/1.67 % (2278077)------------------------------
% 4.94/1.67 % (2278077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.67 % (2278077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.67 % (2278077)CaDiCaL version: 2.1.3
% 4.94/1.67 % (2278077)Termination reason: Instruction limit
% 4.94/1.67 % (2278077)Termination phase: Saturation
% 4.94/1.67 % (2278077)Time elapsed: 0.118 s
% 4.94/1.67 % (2278077)Peak memory usage: 89 MB
% 4.94/1.67 % (2278077)Instructions burned: 130 (million)
% 4.94/1.67 % Exception at run slice level
% 4.94/1.67 User error: GNN currently only supports monomorphic FOL.
% 4.94/1.67 % (2278085)lrs+10_1_sil=8000:sp=occurrence:random_seed=901401348:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 4.94/1.67 % (2278085)Also succeeded, but the first one will report.
% 4.94/1.67 % (2278074)Refutation found. Thanks to Tanya!
% 4.94/1.67 % SZS status Theorem for theBenchmark
% 4.94/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 5.97/1.98 % (2278074)------------------------------
% 5.97/1.98 % (2278074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.98 % (2278074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.98 % (2278074)CaDiCaL version: 2.1.3
% 5.97/1.98 % (2278074)Termination reason: Refutation
% 5.97/1.98 % (2278074)Time elapsed: 0.012 s
% 5.97/1.98 % (2278074)Peak memory usage: 89 MB
% 5.97/1.98 % (2278074)Instructions burned: 9 (million)
% 5.97/1.98 % (2278074)------------------------------
% 5.97/1.98 % (2278074)------------------------------
% 5.97/1.98 % (2278062)Success in time 0.714 s
% 5.97/1.98 % Vampire exiting
%------------------------------------------------------------------------------