%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM410+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 12:15:04 PM UTC 2026
% Result : Theorem 3.37s 1.35s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% 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 : 110 ( 47 ~; 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 : 23 ( 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/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/sandbox/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] :
( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f123,plain,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(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(f219,plain,
( ~ subset(relation_rng(sK16),relation_rng(sK16))
| ~ relation(sK16)
| ~ function(sK16)
| ~ transfinite_sequence(sK16) ),
inference(resolution,[],[f123,f188]) ).
fof(f220,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ~ transfinite_sequence(sK16) ),
inference(forward_subsumption_resolution,[],[f219,f180]) ).
fof(f221,plain,
( ~ function(sK16)
| ~ transfinite_sequence(sK16) ),
inference(forward_subsumption_resolution,[],[f220,f186]) ).
fof(f222,plain,
~ transfinite_sequence(sK16),
inference(forward_subsumption_resolution,[],[f221,f185]) ).
fof(f223,plain,
( ~ ordinal(relation_dom(sK16))
| ~ relation(sK16)
| ~ function(sK16) ),
inference(resolution,[],[f222,f121]) ).
fof(f225,plain,
( ~ relation(sK16)
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f223,f187]) ).
fof(f226,plain,
~ function(sK16),
inference(forward_subsumption_resolution,[],[f225,f186]) ).
fof(f227,plain,
$false,
inference(forward_subsumption_resolution,[],[f226,f185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM410+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 19:51:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.37/1.35 % (1974922)Detected formulas, will run a generic FOF schedule.
% 3.37/1.35 % (1974931)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2205648382:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.37/1.35 % (1974931)Refutation not found, incomplete strategy
% 3.37/1.35 % (1974931)------------------------------
% 3.37/1.35 % (1974931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (1974931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (1974931)CaDiCaL version: 2.1.3
% 3.37/1.35 % (1974931)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.35 % (1974931)Time elapsed: 0.001 s
% 3.37/1.35 % (1974931)Peak memory usage: 88 MB
% 3.37/1.35 % (1974931)Instructions burned: 1 (million)
% 3.37/1.35 % (1974933)dis-21_1_sil=8000:lcm=predicate:random_seed=4025116449: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)
% 3.37/1.35 % (1974930)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3303498809:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.37/1.35 % (1974932)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3217374197:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.37/1.35 % (1974927)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=2157797601:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.37/1.35 % (1974928)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=1023314362:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.37/1.35 % (1974929)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=3661833160:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.37/1.35 % (1974930)Refutation not found, incomplete strategy
% 3.37/1.35 % (1974930)------------------------------
% 3.37/1.35 % (1974930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (1974930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (1974930)CaDiCaL version: 2.1.3
% 3.37/1.35 % (1974930)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.35 % (1974930)Time elapsed: 0.001 s
% 3.37/1.35 % (1974930)Peak memory usage: 88 MB
% 3.37/1.35 % (1974930)Instructions burned: 1 (million)
% 3.37/1.35 % (1974932)First to succeed.
% 3.37/1.35 % (1974932)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1974922"
% 3.37/1.35 % (1974933)Also succeeded, but the first one will report.
% 3.37/1.35 % (1974931)------------------------------
% 3.37/1.35 % (1974931)------------------------------
% 3.37/1.35 % (1974941)lrs+10_1_sil=8000:sp=occurrence:random_seed=848445930:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.37/1.35 % (1974941)Also succeeded, but the first one will report.
% 3.37/1.35 % (1974930)------------------------------
% 3.37/1.35 % (1974930)------------------------------
% 3.37/1.35 % (1974932)Refutation found. Thanks to Tanya!
% 3.37/1.35 % SZS status Theorem for theBenchmark
% 3.37/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.35 % (1974932)------------------------------
% 3.37/1.35 % (1974932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (1974932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (1974932)CaDiCaL version: 2.1.3
% 3.37/1.35 % (1974932)Termination reason: Refutation
% 3.37/1.35 % (1974932)Time elapsed: 0.004 s
% 3.37/1.35 % (1974932)Peak memory usage: 89 MB
% 3.37/1.35 % (1974932)Instructions burned: 4 (million)
% 3.37/1.35 % (1974932)------------------------------
% 3.37/1.35 % (1974932)------------------------------
% 3.37/1.35 % (1974922)Success in time 0.41 s
% 3.37/1.35 % Vampire exiting
%------------------------------------------------------------------------------