%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW496_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 : n014.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 01:30:41 PM UTC 2026
% Result : Theorem 4.63s 1.63s
% Output : Refutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 6 unt; 0 typ; 6 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 149 ( 65 ~; 60 |; 11 &)
% ( 8 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 19 usr; 7 prp; 0-4 aty)
% Number of functors : 32 ( 32 usr; 17 con; 0-4 aty)
% Number of variables : 17 ( 0 sgn 11 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
real: $tType ).
tff(type_def_7,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_1,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_3,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_4,type,
fFalse: bool ).
tff(func_def_5,type,
fTrue: bool ).
tff(func_def_6,type,
l: real ).
tff(func_def_7,type,
p: fun(real,bool) ).
tff(func_def_8,type,
y1: real ).
tff(func_def_9,type,
x: real ).
tff(func_def_10,type,
y: real ).
tff(func_def_11,type,
sK0: real ).
tff(func_def_12,type,
sK1: real ).
tff(func_def_13,type,
sK2: real ).
tff(func_def_14,type,
sK3: real ).
tff(func_def_15,type,
sK4: real ).
tff(func_def_16,type,
sK5: real ).
tff(func_def_17,type,
sK6: real ).
tff(func_def_18,type,
sK7: real ).
tff(func_def_19,type,
sK8:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_20,type,
sK9: real ).
tff(func_def_21,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_22,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_23,type,
sK12:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_24,type,
sK13:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_25,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_26,type,
sK15:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_27,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_28,type,
sK17:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_29,type,
sK18:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_30,type,
sK19: real ).
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,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
isLub:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * X0 ) > $o ) ).
tff(pred_def_8,type,
isUb:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * X0 ) > $o ) ).
tff(pred_def_9,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_10,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(pred_def_13,type,
sQ20_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f4,axiom,
! [X0: real] :
( pp(aa(real,bool,p,X0))
=> ( ord_less(real,y,X0)
=> ord_less(real,y,l) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096_B_Bz_O_A_091_124_AP_Az_059_Ay_A_060_Az_A_124_093_A_061_061_062_Ay_A_060_AL_096) ).
tff(f5,axiom,
( ord_less(real,y,l)
=> ~ ! [X0: real] :
( pp(aa(real,bool,p,X0))
=> ~ ord_less(real,y,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096_091_124_Ay_A_060_AL_059_AALL_Az_O_AP_Az_A_N_N_062_A_126_Ay_A_060_Az_A_124_093_A_061_061_062_AFalse_096) ).
tff(f120,conjecture,
( ? [X0: real] :
( pp(aa(real,bool,p,X0))
& ord_less(real,y,X0) )
<=> ord_less(real,y,l) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f121,negated_conjecture,
~ ( ? [X0: real] :
( pp(aa(real,bool,p,X0))
& ord_less(real,y,X0) )
<=> ord_less(real,y,l) ),
inference(negated_conjecture,[status(cth)],[f120]) ).
tff(f124,plain,
! [X0: real] :
( ord_less(real,y,l)
| ~ ord_less(real,y,X0)
| ~ pp(aa(real,bool,p,X0)) ),
inference(ennf_transformation,[],[f4]) ).
tff(f125,plain,
! [X0: real] :
( ord_less(real,y,l)
| ~ ord_less(real,y,X0)
| ~ pp(aa(real,bool,p,X0)) ),
inference(flattening,[],[f124]) ).
tff(f126,plain,
( ? [X0: real] :
( ord_less(real,y,X0)
& pp(aa(real,bool,p,X0)) )
| ~ ord_less(real,y,l) ),
inference(ennf_transformation,[],[f5]) ).
tff(f237,plain,
( ? [X0: real] :
( pp(aa(real,bool,p,X0))
& ord_less(real,y,X0) )
<~> ord_less(real,y,l) ),
inference(ennf_transformation,[],[f121]) ).
tff(f240,plain,
( ( ord_less(real,y,sK2)
& pp(aa(real,bool,p,sK2)) )
| ~ ord_less(real,y,l) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f126]) ).
tff(f284,plain,
( ( ~ ord_less(real,y,l)
| ! [X0: real] :
( ~ pp(aa(real,bool,p,X0))
| ~ ord_less(real,y,X0) ) )
& ( ord_less(real,y,l)
| ? [X0: real] :
( pp(aa(real,bool,p,X0))
& ord_less(real,y,X0) ) ) ),
inference(nnf_transformation,[],[f237]) ).
tff(f285,plain,
( ( ~ ord_less(real,y,l)
| ! [X0: real] :
( ~ pp(aa(real,bool,p,X0))
| ~ ord_less(real,y,X0) ) )
& ( ord_less(real,y,l)
| ? [X1: real] :
( pp(aa(real,bool,p,X1))
& ord_less(real,y,X1) ) ) ),
inference(rectify,[],[f284]) ).
tff(f286,plain,
( ( ~ ord_less(real,y,l)
| ! [X0: real] :
( ~ pp(aa(real,bool,p,X0))
| ~ ord_less(real,y,X0) ) )
& ( ord_less(real,y,l)
| ( pp(aa(real,bool,p,sK19))
& ord_less(real,y,sK19) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X1,sK19)],[f285]) ).
tff(f290,plain,
! [X0: real] :
( ord_less(real,y,l)
| ~ ord_less(real,y,X0)
| ~ pp(aa(real,bool,p,X0)) ),
inference(cnf_transformation,[],[f125]) ).
tff(f291,plain,
( pp(aa(real,bool,p,sK2))
| ~ ord_less(real,y,l) ),
inference(cnf_transformation,[],[f240]) ).
tff(f292,plain,
( ord_less(real,y,sK2)
| ~ ord_less(real,y,l) ),
inference(cnf_transformation,[],[f240]) ).
tff(f442,plain,
( ord_less(real,y,l)
| ord_less(real,y,sK19) ),
inference(cnf_transformation,[],[f286]) ).
tff(f443,plain,
( ord_less(real,y,l)
| pp(aa(real,bool,p,sK19)) ),
inference(cnf_transformation,[],[f286]) ).
tff(f444,plain,
! [X0: real] :
( ~ ord_less(real,y,l)
| ~ pp(aa(real,bool,p,X0))
| ~ ord_less(real,y,X0) ),
inference(cnf_transformation,[],[f286]) ).
tff(f506,definition,
( spl21_1
<=> ord_less(real,y,sK19) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
tff(f507,plain,
( ord_less(real,y,sK19)
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f506]) ).
tff(f509,definition,
( spl21_2
<=> ord_less(real,y,l) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
tff(f511,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f442,f509,f506]) ).
tff(f513,definition,
( spl21_3
<=> pp(aa(real,bool,p,sK19)) ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
tff(f514,plain,
( pp(aa(real,bool,p,sK19))
| ~ spl21_3 ),
inference(avatar_component_clause,[],[f513]) ).
tff(f515,plain,
( spl21_3
| spl21_2 ),
inference(avatar_split_clause,[],[f443,f509,f513]) ).
tff(f517,definition,
( spl21_4
<=> ! [X0: real] :
( ~ pp(aa(real,bool,p,X0))
| ~ ord_less(real,y,X0) ) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
tff(f518,plain,
( ! [X0: real] :
( ~ pp(aa(real,bool,p,X0))
| ~ ord_less(real,y,X0) )
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f517]) ).
tff(f520,plain,
( spl21_4
| ~ spl21_2 ),
inference(avatar_split_clause,[],[f444,f509,f517]) ).
tff(f530,definition,
( spl21_7
<=> pp(aa(real,bool,p,sK2)) ),
introduced(definition,[new_symbols(definition,[spl21_7])],[avatar_definition]) ).
tff(f531,plain,
( pp(aa(real,bool,p,sK2))
| ~ spl21_7 ),
inference(avatar_component_clause,[],[f530]) ).
tff(f532,plain,
( ~ spl21_2
| spl21_7 ),
inference(avatar_split_clause,[],[f291,f530,f509]) ).
tff(f534,definition,
( spl21_8
<=> ord_less(real,y,sK2) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
tff(f535,plain,
( ord_less(real,y,sK2)
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f534]) ).
tff(f536,plain,
( ~ spl21_2
| spl21_8 ),
inference(avatar_split_clause,[],[f292,f534,f509]) ).
tff(f537,plain,
( spl21_4
| spl21_2 ),
inference(avatar_split_clause,[],[f290,f509,f517]) ).
tff(f538,plain,
( ~ ord_less(real,y,sK2)
| ~ spl21_4
| ~ spl21_7 ),
inference(resolution,[],[f531,f518]) ).
tff(f539,plain,
( $false
| ~ spl21_4
| ~ spl21_7
| ~ spl21_8 ),
inference(resolution,[],[f538,f535]) ).
tff(f540,plain,
( ~ spl21_4
| ~ spl21_7
| ~ spl21_8 ),
inference(avatar_contradiction_clause,[],[f539]) ).
tff(f541,plain,
( ~ ord_less(real,y,sK19)
| ~ spl21_3
| ~ spl21_4 ),
inference(resolution,[],[f514,f518]) ).
tff(f542,plain,
( $false
| ~ spl21_1
| ~ spl21_3
| ~ spl21_4 ),
inference(resolution,[],[f541,f507]) ).
tff(f543,plain,
( ~ spl21_1
| ~ spl21_3
| ~ spl21_4 ),
inference(avatar_contradiction_clause,[],[f542]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f511]) ).
cnf(s2,plain,
( spl21_2
| spl21_3 ),
inference(sat_conversion,[],[f515]) ).
cnf(s3,plain,
( ~ spl21_2
| spl21_4 ),
inference(sat_conversion,[],[f520]) ).
cnf(s8,plain,
( ~ spl21_2
| spl21_7 ),
inference(sat_conversion,[],[f532]) ).
cnf(s9,plain,
( ~ spl21_2
| spl21_8 ),
inference(sat_conversion,[],[f536]) ).
cnf(s10,plain,
( spl21_2
| spl21_4 ),
inference(sat_conversion,[],[f537]) ).
cnf(s11,plain,
( ~ spl21_4
| ~ spl21_7
| ~ spl21_8 ),
inference(sat_conversion,[],[f540]) ).
cnf(s12,plain,
( ~ spl21_1
| ~ spl21_3
| ~ spl21_4 ),
inference(sat_conversion,[],[f543]) ).
cnf(s13,plain,
~ spl21_2,
inference(rat,[],[s11,s3,s8,s9]) ).
cnf(s14,plain,
spl21_4,
inference(rat,[],[s10,s13]) ).
cnf(s15,plain,
spl21_3,
inference(rat,[],[s2,s13]) ).
cnf(s16,plain,
spl21_1,
inference(rat,[],[s1,s13]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s12,s16,s14,s15]) ).
tff(f544,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW496_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n014.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Mon Sep 28 14:14:46 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.31 Running first-order theorem proving
% 0.27/0.31 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
% 4.63/1.63 % (1796012)Detected formulas, will run a generic FOF schedule.
% 4.63/1.63 % (1796027)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=1263787020:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.63/1.63 % (1796033)dis-21_1_sil=8000:lcm=predicate:random_seed=1361653068: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)
% 4.63/1.63 % (1796033)First to succeed.
% 4.63/1.63 % (1796033)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1796012"
% 4.63/1.63 % (1796028)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=496250142:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.63/1.63 % (1796031)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2786243334:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.63/1.63 % (1796029)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=981307688:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.63/1.63 % (1796031)Also succeeded, but the first one will report.
% 4.63/1.63 % (1796029)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.63/1.63 % (1796032)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1072980138:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.63/1.63 % (1796032)Also succeeded, but the first one will report.
% 4.63/1.63 % (1796030)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1583140731:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.63/1.63 % (1796030)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.63/1.63 % (1796030)Also succeeded, but the first one will report.
% 4.63/1.63 % Exception at run slice level
% 4.63/1.63 User error: GNN currently only supports monomorphic FOL.
% 4.63/1.63 % (1796033)Refutation found. Thanks to Tanya!
% 4.63/1.63 % SZS status Theorem for theBenchmark
% 4.63/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 4.63/1.64 % (1796033)------------------------------
% 4.63/1.64 % (1796033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.64 % (1796033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.64 % (1796033)CaDiCaL version: 2.1.3
% 4.63/1.64 % (1796033)Termination reason: Refutation
% 4.63/1.64 % (1796033)Time elapsed: 0.007 s
% 4.63/1.64 % (1796033)Peak memory usage: 89 MB
% 4.63/1.64 % (1796033)Instructions burned: 8 (million)
% 4.63/1.64 % (1796033)------------------------------
% 4.63/1.64 % (1796033)------------------------------
% 4.63/1.64 % (1796012)Success in time 0.538 s
% 4.63/1.64 % Vampire exiting
%------------------------------------------------------------------------------