%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM394+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 12:24:06 PM UTC 2026
% Result : Theorem 0.12s 0.48s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 18 unt; 2 def)
% Number of atoms : 124 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 123 ( 50 ~; 46 |; 11 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 43 ( 1 sgn 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f24,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(f26,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f28,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X0,X1)
& X0 != X1
& ~ in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f29,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( ordinal_subset(X0,X1)
| in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_ordinal1) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( ordinal_subset(X0,X1)
| in(X1,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f26]) ).
fof(f47,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f55,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f57,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f56]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ~ ordinal_subset(X0,X1)
& ~ in(X1,X0)
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( ~ ordinal_subset(X0,X1)
& ~ in(X1,X0)
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f63]) ).
fof(f76,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0,X1] :
( ~ in(X1,X0)
| subset(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f110,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f113,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f115,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f116,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f64]) ).
fof(f117,plain,
~ in(sK14,sK13),
inference(cnf_transformation,[],[f64]) ).
fof(f118,plain,
~ ordinal_subset(sK13,sK14),
inference(cnf_transformation,[],[f64]) ).
fof(f119,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f64]) ).
fof(f131,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(consistent_polarity_flipping,[],[f80]) ).
fof(f139,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X0)
| subset(X0,X1)
| ~ ordinal(X1) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f141,plain,
! [X0] : ~ subset(X0,X0),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f143,plain,
ordinal_subset(sK13,sK14),
inference(consistent_polarity_flipping,[],[f118]) ).
fof(f165,plain,
epsilon_transitive(sK14),
inference(resolution,[],[f76,f116]) ).
fof(f203,plain,
( ~ ordinal(sK13)
| subset(sK13,sK14)
| ~ ordinal(sK14) ),
inference(resolution,[],[f139,f143]) ).
fof(f204,plain,
( subset(sK13,sK14)
| ~ ordinal(sK14) ),
inference(forward_subsumption_resolution,[],[f203,f119]) ).
fof(f205,plain,
subset(sK13,sK14),
inference(forward_subsumption_resolution,[],[f204,f116]) ).
fof(f209,plain,
! [X0] :
( ~ ordinal(X0)
| in(sK13,X0)
| sK13 = X0
| in(X0,sK13) ),
inference(resolution,[],[f115,f119]) ).
fof(f212,plain,
( ~ in(sK13,sK14)
| ~ epsilon_transitive(sK14) ),
inference(resolution,[],[f205,f131]) ).
fof(f214,plain,
~ in(sK13,sK14),
inference(forward_subsumption_resolution,[],[f212,f165]) ).
fof(f234,definition,
( spl15_6
<=> in(sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
fof(f238,definition,
( spl15_7
<=> sK13 = sK14 ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f240,plain,
( sK13 = sK14
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f242,plain,
( in(sK13,sK14)
| sK13 = sK14
| in(sK14,sK13) ),
inference(resolution,[],[f209,f116]) ).
fof(f259,plain,
( in(sK13,sK14)
| sK13 = sK14 ),
inference(forward_subsumption_resolution,[],[f242,f117]) ).
fof(f260,plain,
( spl15_7
| spl15_6 ),
inference(avatar_split_clause,[],[f259,f234,f238]) ).
fof(f263,plain,
~ spl15_6,
inference(avatar_split_clause,[],[f214,f234]) ).
fof(f334,plain,
( subset(sK13,sK13)
| ~ spl15_7 ),
inference(superposition,[],[f205,f240]) ).
fof(f341,plain,
( $false
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f334,f141]) ).
fof(f342,plain,
~ spl15_7,
inference(avatar_contradiction_clause,[],[f341]) ).
cnf(s8,plain,
( spl15_6
| spl15_7 ),
inference(sat_conversion,[],[f260]) ).
cnf(s9,plain,
~ spl15_6,
inference(sat_conversion,[],[f263]) ).
cnf(s24,plain,
~ spl15_7,
inference(sat_conversion,[],[f342]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s8,s24,s9]) ).
fof(f343,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % 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
% 0.12/0.39 % DateTime : Sun Sep 27 19:46:55 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.12/0.48 % (1553522)Will run a generic schedule for satisfiability detection.
% 0.12/0.48 % (1553527)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1945297703_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.48 % TRYING [1]
% 0.12/0.48 % TRYING [2]
% 0.12/0.48 % TRYING [3]
% 0.12/0.48 % TRYING [4]
% 0.12/0.48 % (1553528)% WARNING: option uhcvi not known.
% 0.12/0.48 % TRYING [5]
% 0.12/0.48 % TRYING [6]
% 0.12/0.48 % (1553528)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4004002814:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.48 % (1553529)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=239651079:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.48 % (1553530)dis+10_1_sil=32000:sp=arity:random_seed=771691334:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.48 % (1553532)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=861581926:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.48 % (1553531)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=857593599:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.48 % (1553533)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2026016343:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.48 % TRYING [7]
% 0.12/0.48 % (1553531) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1553522-1553531"...
% 0.12/0.48 % (1553530) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1553522-1553530"...
% 0.12/0.48 % (1553528) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1553522-1553528"...
% 0.12/0.48 % (1553532) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1553522-1553532"...
% 0.12/0.48 % (1553531)...printing done.
% 0.12/0.48 % (1553530)...printing done.
% 0.12/0.48 % (1553528)...printing done.
% 0.12/0.48 % (1553532)...printing done.
% 0.12/0.48 % (1553528)Refutation found. Thanks to Tanya!
% 0.12/0.48 % SZS status Theorem for theBenchmark
% 0.12/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.48 % (1553528)------------------------------
% 0.12/0.48 % (1553528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.48 % (1553528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.48 % (1553528)CaDiCaL version: 2.1.3
% 0.12/0.48 % (1553528)Termination reason: Refutation
% 0.12/0.48 % (1553528)Time elapsed: 0.007 s
% 0.12/0.48 % (1553528)Peak memory usage: 12 MB
% 0.12/0.48 % (1553528)Instructions burned: 7 (million)
% 0.12/0.48 % (1553522)Success in time 0.047 s
% 0.12/0.48 % Vampire exiting
%------------------------------------------------------------------------------