%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 0.07s 0.38s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 106 ( 43 ~; 35 |; 16 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 24 ( 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1)
& transfinite_sequence(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f40,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ordinal(relation_dom(X0))
=> transfinite_sequence_of(X0,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ordinal(relation_dom(X0))
=> transfinite_sequence_of(X0,relation_rng(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f67,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f68,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f70,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(flattening,[],[f69]) ).
fof(f81,plain,
? [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(X0))
& ordinal(relation_dom(X0))
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
? [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(X0))
& ordinal(relation_dom(X0))
& relation(X0)
& function(X0) ),
inference(flattening,[],[f81]) ).
fof(f89,plain,
! [X0] :
( ( ( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0)) )
& ( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f68]) ).
fof(f90,plain,
! [X0,X1] :
( ( ( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0) )
& ( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(nnf_transformation,[],[f70]) ).
fof(f108,plain,
( ~ transfinite_sequence_of(sK16,relation_rng(sK16))
& ordinal(relation_dom(sK16))
& relation(sK16)
& function(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f82]) ).
fof(f121,plain,
! [X0] :
( ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f123,plain,
! [X0,X1] :
( ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f180,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f185,plain,
function(sK16),
inference(cnf_transformation,[],[f108]) ).
fof(f186,plain,
relation(sK16),
inference(cnf_transformation,[],[f108]) ).
fof(f187,plain,
ordinal(relation_dom(sK16)),
inference(cnf_transformation,[],[f108]) ).
fof(f188,plain,
~ transfinite_sequence_of(sK16,relation_rng(sK16)),
inference(cnf_transformation,[],[f108]) ).
fof(f303,plain,
( transfinite_sequence(sK16)
| ~ relation(sK16)
| ~ function(sK16) ),
inference(resolution,[],[f121,f187]) ).
fof(f306,plain,
( transfinite_sequence(sK16)
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f303,f186]) ).
fof(f307,plain,
transfinite_sequence(sK16),
inference(forward_subsumption_resolution,[],[f306,f185]) ).
fof(f334,plain,
! [X0] :
( transfinite_sequence_of(X0,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0) ),
inference(resolution,[],[f123,f180]) ).
fof(f430,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ~ transfinite_sequence(sK16) ),
inference(resolution,[],[f334,f188]) ).
fof(f436,plain,
( ~ function(sK16)
| ~ transfinite_sequence(sK16) ),
inference(forward_subsumption_resolution,[],[f430,f186]) ).
fof(f438,plain,
~ transfinite_sequence(sK16),
inference(forward_subsumption_resolution,[],[f436,f185]) ).
fof(f440,plain,
$false,
inference(forward_subsumption_resolution,[],[f438,f307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 19:48:19 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.34 Running first-order model finding
% 0.07/0.34 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.38 % (2693992)Will run a generic schedule for satisfiability detection.
% 0.07/0.38 % (2693998)% WARNING: option uhcvi not known.
% 0.07/0.38 % (2694001)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1265630870:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.38 % (2693999)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=754340874:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.38 % (2693997)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3409263129_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.38 % (2694000)dis+10_1_sil=32000:sp=arity:random_seed=3081288280:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.38 % (2693998)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1430403504:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.38 % (2694002)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3498871914:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.38 % (2694003)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2649780017:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.38 % TRYING [1]
% 0.07/0.38 % TRYING [2]
% 0.07/0.38 % TRYING [3]
% 0.07/0.38 % TRYING [4]
% 0.07/0.38 % (2694000) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2693992-2694000"...
% 0.07/0.38 % (2693998) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2693992-2693998"...
% 0.07/0.38 % (2694002) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2693992-2694002"...
% 0.07/0.38 % TRYING [5]
% 0.07/0.38 % (2694000)...printing done.
% 0.07/0.38 % (2693998)...printing done.
% 0.07/0.38 % (2694002)...printing done.
% 0.07/0.38 % (2694000)Refutation found. Thanks to Tanya!
% 0.07/0.38 % SZS status Theorem for theBenchmark
% 0.07/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.38 % (2694000)------------------------------
% 0.07/0.38 % (2694000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.38 % (2694000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.38 % (2694000)CaDiCaL version: 2.1.3
% 0.07/0.38 % (2694000)Termination reason: Refutation
% 0.07/0.38 % (2694000)Time elapsed: 0.003 s
% 0.07/0.38 % (2694000)Peak memory usage: 12 MB
% 0.07/0.38 % (2694000)Instructions burned: 8 (million)
% 0.07/0.38 % (2693992)Success in time 0.036 s
% 0.07/0.38 % Vampire exiting
%------------------------------------------------------------------------------