%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:15:03 PM UTC 2026
% Result : Theorem 2.25s 1.07s
% Output : Refutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 13 unt; 3 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 137 ( 55 ~; 58 |; 11 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 42 ( 0 sgn 40 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f8,axiom,
! [X0,X1] :
( inclusion_comparable(X0,X1)
<=> ( subset(X0,X1)
| subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(f24,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f30,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> inclusion_comparable(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_ordinal1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> inclusion_comparable(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f55,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f56,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f58,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f57]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ~ inclusion_comparable(X0,X1)
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f72,plain,
! [X0,X1] :
( ( inclusion_comparable(X0,X1)
| ( ~ subset(X0,X1)
& ~ subset(X1,X0) ) )
& ( subset(X0,X1)
| subset(X1,X0)
| ~ inclusion_comparable(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f73,plain,
! [X0,X1] :
( ( inclusion_comparable(X0,X1)
| ( ~ subset(X0,X1)
& ~ subset(X1,X0) ) )
& ( subset(X0,X1)
| subset(X1,X0)
| ~ inclusion_comparable(X0,X1) ) ),
inference(flattening,[],[f72]) ).
fof(f86,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f58]) ).
fof(f87,plain,
( ~ inclusion_comparable(sK12,sK13)
& ordinal(sK13)
& ordinal(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f63]) ).
fof(f97,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f99,plain,
! [X0,X1] :
( inclusion_comparable(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f100,plain,
! [X0,X1] :
( inclusion_comparable(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f128,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
ordinal(sK12),
inference(cnf_transformation,[],[f87]) ).
fof(f136,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f137,plain,
~ inclusion_comparable(sK12,sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f161,plain,
~ subset(sK13,sK12),
inference(resolution,[],[f99,f137]) ).
fof(f162,plain,
~ subset(sK12,sK13),
inference(resolution,[],[f100,f137]) ).
fof(f183,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f128,f97]) ).
fof(f184,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f183]) ).
fof(f189,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f184,f128]) ).
fof(f190,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f189]) ).
fof(f315,plain,
( ~ ordinal(sK13)
| subset(sK12,sK13)
| ~ ordinal(sK12) ),
inference(resolution,[],[f190,f161]) ).
fof(f317,definition,
( spl15_19
<=> ordinal(sK12) ),
introduced(definition,[new_symbols(definition,[spl15_19])],[avatar_definition]) ).
fof(f318,plain,
( ~ ordinal(sK12)
| spl15_19 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f320,definition,
( spl15_20
<=> subset(sK12,sK13) ),
introduced(definition,[new_symbols(definition,[spl15_20])],[avatar_definition]) ).
fof(f321,plain,
( subset(sK12,sK13)
| ~ spl15_20 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f323,definition,
( spl15_21
<=> ordinal(sK13) ),
introduced(definition,[new_symbols(definition,[spl15_21])],[avatar_definition]) ).
fof(f324,plain,
( ~ ordinal(sK13)
| spl15_21 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f325,plain,
( ~ spl15_19
| spl15_20
| ~ spl15_21 ),
inference(avatar_split_clause,[],[f315,f323,f320,f317]) ).
fof(f363,plain,
( $false
| spl15_19 ),
inference(resolution,[],[f318,f135]) ).
fof(f364,plain,
spl15_19,
inference(avatar_contradiction_clause,[],[f363]) ).
fof(f365,plain,
( $false
| spl15_21 ),
inference(resolution,[],[f324,f136]) ).
fof(f366,plain,
spl15_21,
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f367,plain,
( $false
| ~ spl15_20 ),
inference(resolution,[],[f321,f162]) ).
fof(f368,plain,
~ spl15_20,
inference(avatar_contradiction_clause,[],[f367]) ).
cnf(s12,plain,
( ~ spl15_19
| spl15_20
| ~ spl15_21 ),
inference(sat_conversion,[],[f325]) ).
cnf(s20,plain,
spl15_19,
inference(sat_conversion,[],[f364]) ).
cnf(s21,plain,
spl15_21,
inference(sat_conversion,[],[f366]) ).
cnf(s22,plain,
~ spl15_20,
inference(sat_conversion,[],[f368]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s12,s21,s22,s20]) ).
fof(f369,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 19:45:56 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.25/1.07 % (3274197)Detected formulas, will run a generic FOF schedule.
% 2.25/1.07 % (3274208)dis-21_1_sil=8000:lcm=predicate:random_seed=2375249362: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)
% 2.25/1.07 % (3274208)First to succeed.
% 2.25/1.07 % (3274208)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3274197"
% 2.25/1.07 % (3274206)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2083277751:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.25/1.07 % (3274202)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=3652786880:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.25/1.07 % (3274204)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=413218015:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.25/1.07 % (3274207)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=553073681:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.25/1.07 % (3274205)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1155821504:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.25/1.07 % (3274203)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=556603388:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.25/1.07 % (3274205)Refutation not found, incomplete strategy
% 2.25/1.07 % (3274205)------------------------------
% 2.25/1.07 % (3274205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.25/1.07 % (3274205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/1.07 % (3274205)CaDiCaL version: 2.1.3
% 2.25/1.07 % (3274206)Refutation not found, incomplete strategy
% 2.25/1.07 % (3274206)------------------------------
% 2.25/1.07 % (3274206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.25/1.07 % (3274205)Termination reason: Refutation not found, incomplete strategy
% 2.25/1.07 % (3274205)Time elapsed: 0.001 s
% 2.25/1.07 % (3274205)Peak memory usage: 88 MB
% 2.25/1.07 % (3274206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/1.07 % (3274206)CaDiCaL version: 2.1.3
% 2.25/1.07 % (3274206)Termination reason: Refutation not found, incomplete strategy
% 2.25/1.07 % (3274206)Time elapsed: 0.001 s
% 2.25/1.07 % (3274206)Peak memory usage: 87 MB
% 2.25/1.07 % (3274207)Also succeeded, but the first one will report.
% 2.25/1.07 % (3274208)Refutation found. Thanks to Tanya!
% 2.25/1.07 % SZS status Theorem for theBenchmark
% 2.25/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 2.25/1.07 % (3274208)------------------------------
% 2.25/1.07 % (3274208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.25/1.07 % (3274208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/1.07 % (3274208)CaDiCaL version: 2.1.3
% 2.25/1.07 % (3274208)Termination reason: Refutation
% 2.25/1.07 % (3274208)Time elapsed: 0.003 s
% 2.25/1.07 % (3274208)Peak memory usage: 89 MB
% 2.25/1.07 % (3274208)Instructions burned: 6 (million)
% 2.25/1.07 % (3274208)------------------------------
% 2.25/1.07 % (3274208)------------------------------
% 2.25/1.07 % (3274197)Success in time 0.26 s
% 2.25/1.07 % Vampire exiting
%------------------------------------------------------------------------------