%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:15:05 PM UTC 2026
% Result : Theorem 3.66s 1.49s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 19 unt; 7 def)
% Number of atoms : 178 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 192 ( 83 ~; 70 |; 21 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 50 ( 0 sgn 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( subset(X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f31,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f38,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ proper_subset(X0,X1)
& X0 != X1
& ~ proper_subset(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_ordinal1) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ proper_subset(X0,X1)
& X0 != X1
& ~ proper_subset(X1,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f46,plain,
! [X0,X1] :
( ( subset(X0,X1)
& X0 != X1 )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f67,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f46]) ).
fof(f70,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f72,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f71]) ).
fof(f80,plain,
? [X0] :
( ? [X1] :
( ~ proper_subset(X0,X1)
& X0 != X1
& ~ proper_subset(X1,X0)
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f81,plain,
? [X0] :
( ? [X1] :
( ~ proper_subset(X0,X1)
& X0 != X1
& ~ proper_subset(X1,X0)
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f80]) ).
fof(f101,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f72]) ).
fof(f103,plain,
( ~ proper_subset(sK15,sK16)
& sK15 != sK16
& ~ proper_subset(sK16,sK15)
& ordinal(sK16)
& ordinal(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X1,sK16)],[f81]) ).
fof(f116,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f164,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f173,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f174,plain,
ordinal(sK16),
inference(cnf_transformation,[],[f103]) ).
fof(f175,plain,
~ proper_subset(sK16,sK15),
inference(cnf_transformation,[],[f103]) ).
fof(f176,plain,
sK15 != sK16,
inference(cnf_transformation,[],[f103]) ).
fof(f177,plain,
~ proper_subset(sK15,sK16),
inference(cnf_transformation,[],[f103]) ).
fof(f182,definition,
! [X0,X1] :
( sQ17_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ17_eqProxy])],[equality_proxy_definition]) ).
fof(f183,plain,
! [X0,X1] :
( sQ17_eqProxy(X0,X1)
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(equality_proxy_replacement,[],[f117,f182]) ).
fof(f184,plain,
~ sQ17_eqProxy(sK15,sK16),
inference(equality_proxy_replacement,[],[f176,f182]) ).
fof(f188,plain,
! [X0,X1] :
( sQ17_eqProxy(X1,X0)
| ~ sQ17_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f182]) ).
fof(f204,plain,
~ sQ17_eqProxy(sK16,sK15),
inference(resolution,[],[f188,f184]) ).
fof(f225,plain,
( ~ subset(sK15,sK16)
| proper_subset(sK15,sK16) ),
inference(resolution,[],[f183,f184]) ).
fof(f226,plain,
( ~ subset(sK16,sK15)
| proper_subset(sK16,sK15) ),
inference(resolution,[],[f183,f204]) ).
fof(f228,definition,
( spl18_5
<=> proper_subset(sK16,sK15) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f229,plain,
( proper_subset(sK16,sK15)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,definition,
( spl18_6
<=> subset(sK16,sK15) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f233,plain,
( spl18_5
| ~ spl18_6 ),
inference(avatar_split_clause,[],[f226,f231,f228]) ).
fof(f235,definition,
( spl18_7
<=> proper_subset(sK15,sK16) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
fof(f236,plain,
( proper_subset(sK15,sK16)
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,definition,
( spl18_8
<=> subset(sK15,sK16) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
fof(f239,plain,
( ~ subset(sK15,sK16)
| spl18_8 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( spl18_7
| ~ spl18_8 ),
inference(avatar_split_clause,[],[f225,f238,f235]) ).
fof(f244,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f164,f116]) ).
fof(f245,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f244]) ).
fof(f250,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f245,f164]) ).
fof(f251,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f250]) ).
fof(f530,definition,
( spl18_57
<=> ordinal(sK15) ),
introduced(definition,[new_symbols(definition,[spl18_57])],[avatar_definition]) ).
fof(f531,plain,
( ~ ordinal(sK15)
| spl18_57 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f534,definition,
( spl18_58
<=> ordinal(sK16) ),
introduced(definition,[new_symbols(definition,[spl18_58])],[avatar_definition]) ).
fof(f535,plain,
( ~ ordinal(sK16)
| spl18_58 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f553,plain,
( $false
| spl18_57 ),
inference(resolution,[],[f531,f173]) ).
fof(f555,plain,
spl18_57,
inference(avatar_contradiction_clause,[],[f553]) ).
fof(f556,plain,
( $false
| spl18_58 ),
inference(resolution,[],[f535,f174]) ).
fof(f558,plain,
spl18_58,
inference(avatar_contradiction_clause,[],[f556]) ).
fof(f560,plain,
( $false
| ~ spl18_7 ),
inference(resolution,[],[f236,f177]) ).
fof(f561,plain,
~ spl18_7,
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f562,plain,
( ~ ordinal(sK15)
| subset(sK16,sK15)
| ~ ordinal(sK16)
| spl18_8 ),
inference(resolution,[],[f239,f251]) ).
fof(f564,plain,
( ~ spl18_58
| spl18_6
| ~ spl18_57
| spl18_8 ),
inference(avatar_split_clause,[],[f562,f238,f530,f231,f534]) ).
fof(f565,plain,
( $false
| ~ spl18_5 ),
inference(resolution,[],[f229,f175]) ).
fof(f568,plain,
~ spl18_5,
inference(avatar_contradiction_clause,[],[f565]) ).
cnf(s4,plain,
( spl18_5
| ~ spl18_6 ),
inference(sat_conversion,[],[f233]) ).
cnf(s5,plain,
( spl18_7
| ~ spl18_8 ),
inference(sat_conversion,[],[f240]) ).
cnf(s43,plain,
spl18_57,
inference(sat_conversion,[],[f555]) ).
cnf(s44,plain,
spl18_58,
inference(sat_conversion,[],[f558]) ).
cnf(s46,plain,
~ spl18_7,
inference(sat_conversion,[],[f561]) ).
cnf(s47,plain,
( spl18_6
| spl18_8
| ~ spl18_57
| ~ spl18_58 ),
inference(sat_conversion,[],[f564]) ).
cnf(s48,plain,
~ spl18_5,
inference(sat_conversion,[],[f568]) ).
cnf(s56,plain,
~ spl18_8,
inference(rat,[],[s5,s46]) ).
cnf(s57,plain,
spl18_6,
inference(rat,[],[s47,s44,s43,s56]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s4,s57,s48]) ).
fof(f569,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 19:52:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.66/1.49 % (1975322)Detected formulas, will run a generic FOF schedule.
% 3.66/1.49 % (1975331)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2737745178:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.49 % (1975331)Refutation not found, incomplete strategy
% 3.66/1.49 % (1975331)------------------------------
% 3.66/1.49 % (1975331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (1975331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (1975331)CaDiCaL version: 2.1.3
% 3.66/1.49 % (1975331)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.49 % (1975331)Time elapsed: 0.001 s
% 3.66/1.49 % (1975331)Peak memory usage: 88 MB
% 3.66/1.49 % (1975331)Instructions burned: 1 (million)
% 3.66/1.49 % (1975327)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=4187740180:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.49 % (1975329)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=1747954633:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.49 % (1975330)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=559225166:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.49 % (1975333)dis-21_1_sil=8000:lcm=predicate:random_seed=940501502: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)
% 3.66/1.49 % (1975328)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=2251086423:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.49 % (1975330)Refutation not found, incomplete strategy
% 3.66/1.49 % (1975330)------------------------------
% 3.66/1.49 % (1975330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (1975330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (1975330)CaDiCaL version: 2.1.3
% 3.66/1.49 % (1975330)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.49 % (1975330)Time elapsed: 0.001 s
% 3.66/1.49 % (1975330)Peak memory usage: 87 MB
% 3.66/1.49 % (1975333)First to succeed.
% 3.66/1.49 % (1975333)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1975322"
% 3.66/1.49 % (1975332)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1861115469:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.49 % (1975332)Also succeeded, but the first one will report.
% 3.66/1.49 % (1975331)------------------------------
% 3.66/1.49 % (1975331)------------------------------
% 3.66/1.49 % (1975330)------------------------------
% 3.66/1.49 % (1975330)------------------------------
% 3.66/1.49 % (1975341)lrs+10_1_sil=8000:sp=occurrence:random_seed=1020081722:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.66/1.49 % (1975333)Refutation found. Thanks to Tanya!
% 3.66/1.49 % SZS status Theorem for theBenchmark
% 3.66/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.49 % (1975333)------------------------------
% 3.66/1.49 % (1975333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (1975333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (1975333)CaDiCaL version: 2.1.3
% 3.66/1.49 % (1975333)Termination reason: Refutation
% 3.66/1.49 % (1975333)Time elapsed: 0.008 s
% 3.66/1.49 % (1975333)Peak memory usage: 89 MB
% 3.66/1.49 % (1975333)Instructions burned: 9 (million)
% 3.66/1.49 % (1975333)------------------------------
% 3.66/1.49 % (1975333)------------------------------
% 3.66/1.49 % (1975322)Success in time 0.443 s
% 3.66/1.49 % Vampire exiting
%------------------------------------------------------------------------------