%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:24:08 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 12 unt; 3 def)
% Number of atoms : 139 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 152 ( 66 ~; 51 |; 21 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 39 ( 0 sgn 35 !; 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(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f164,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ 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(f309,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal_subset(sK15,X0)
| ordinal_subset(X0,sK15) ),
inference(resolution,[],[f116,f173]) ).
fof(f327,plain,
( ordinal_subset(sK15,sK16)
| ordinal_subset(sK16,sK15) ),
inference(resolution,[],[f309,f174]) ).
fof(f330,definition,
( spl17_3
<=> ordinal_subset(sK16,sK15) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f332,plain,
( ordinal_subset(sK16,sK15)
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f334,definition,
( spl17_4
<=> ordinal_subset(sK15,sK16) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f337,plain,
( spl17_3
| spl17_4 ),
inference(avatar_split_clause,[],[f327,f334,f330]) ).
fof(f384,plain,
! [X0] :
( ~ ordinal(X0)
| subset(sK15,X0)
| ~ ordinal_subset(sK15,X0) ),
inference(resolution,[],[f164,f173]) ).
fof(f385,plain,
! [X0] :
( ~ ordinal(X0)
| subset(sK16,X0)
| ~ ordinal_subset(sK16,X0) ),
inference(resolution,[],[f164,f174]) ).
fof(f469,plain,
( subset(sK15,sK16)
| ~ ordinal_subset(sK15,sK16) ),
inference(resolution,[],[f384,f174]) ).
fof(f471,definition,
( spl17_17
<=> subset(sK15,sK16) ),
introduced(definition,[new_symbols(definition,[spl17_17])],[avatar_definition]) ).
fof(f473,plain,
( subset(sK15,sK16)
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f474,plain,
( ~ spl17_4
| spl17_17 ),
inference(avatar_split_clause,[],[f469,f471,f334]) ).
fof(f509,plain,
( subset(sK16,sK15)
| ~ ordinal_subset(sK16,sK15) ),
inference(resolution,[],[f385,f173]) ).
fof(f511,plain,
( subset(sK16,sK15)
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f509,f332]) ).
fof(f658,plain,
( proper_subset(sK16,sK15)
| sK15 = sK16
| ~ spl17_3 ),
inference(resolution,[],[f511,f117]) ).
fof(f660,plain,
( sK15 = sK16
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f658,f175]) ).
fof(f661,plain,
( $false
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f660,f176]) ).
fof(f662,plain,
~ spl17_3,
inference(avatar_contradiction_clause,[],[f661]) ).
fof(f726,plain,
( proper_subset(sK15,sK16)
| sK15 = sK16
| ~ spl17_17 ),
inference(resolution,[],[f473,f117]) ).
fof(f728,plain,
( sK15 = sK16
| ~ spl17_17 ),
inference(forward_subsumption_resolution,[],[f726,f177]) ).
fof(f729,plain,
( $false
| ~ spl17_17 ),
inference(forward_subsumption_resolution,[],[f728,f176]) ).
fof(f730,plain,
~ spl17_17,
inference(avatar_contradiction_clause,[],[f729]) ).
cnf(s2,plain,
( spl17_3
| spl17_4 ),
inference(sat_conversion,[],[f337]) ).
cnf(s17,plain,
( ~ spl17_4
| spl17_17 ),
inference(sat_conversion,[],[f474]) ).
cnf(s49,plain,
~ spl17_3,
inference(sat_conversion,[],[f662]) ).
cnf(s53,plain,
~ spl17_17,
inference(sat_conversion,[],[f730]) ).
cnf(s54,plain,
~ spl17_4,
inference(rat,[],[s17,s53]) ).
cnf(s55,plain,
$false,
inference(rat,[],[s2,s54,s49]) ).
fof(f731,plain,
$false,
inference(avatar_sat_refutation,[],[s55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 19:49:25 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.47 % (1556518)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1556528)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4127080394:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1556524)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1556528) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1556518-1556528"...
% 0.17/0.47 % (1556528)...printing done.
% 0.17/0.47 % (1556528)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1556528)------------------------------
% 0.17/0.47 % (1556528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1556528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1556528)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1556528)Termination reason: Refutation
% 0.17/0.47 % (1556528)Time elapsed: 0.005 s
% 0.17/0.47 % (1556528)Peak memory usage: 12 MB
% 0.17/0.47 % (1556528)Instructions burned: 11 (million)
% 0.17/0.47 % (1556518)Success in time 0.041 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------