%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM412+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 : n026.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 : 11
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 126 ( 52 ~; 48 |; 14 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 53 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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(f9,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& transfinite_sequence(X0)
& ordinal(X1) )
=> transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
fof(f11,axiom,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ( relation(X1)
& function(X1)
& transfinite_sequence(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f42,axiom,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( transfinite_sequence_of(X2,X0)
=> transfinite_sequence_of(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(f43,conjecture,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_ordinal1) ).
fof(f44,negated_conjecture,
~ ! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f66,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f67,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f68]) ).
fof(f71,plain,
! [X0,X1] :
( ( relation(X1)
& function(X1)
& transfinite_sequence(X1) )
| ~ transfinite_sequence_of(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f84,plain,
! [X0,X1] :
( ! [X2] :
( transfinite_sequence_of(X2,X1)
| ~ transfinite_sequence_of(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f85,plain,
? [X0,X1] :
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0)
& ordinal(X2) )
& transfinite_sequence_of(X1,X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f92,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,[],[f67]) ).
fof(f110,plain,
( ~ transfinite_sequence_of(tseq_dom_restriction(sK17,sK18),sK16)
& ordinal(sK18)
& transfinite_sequence_of(sK17,sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f85]) ).
fof(f122,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f124,plain,
! [X0,X1] :
( ~ transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f126,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f127,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| function(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f128,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| relation(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ transfinite_sequence_of(X2,X0)
| transfinite_sequence_of(X2,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f194,plain,
transfinite_sequence_of(sK17,sK16),
inference(cnf_transformation,[],[f110]) ).
fof(f195,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f196,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sK17,sK18),sK16),
inference(cnf_transformation,[],[f110]) ).
fof(f202,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(forward_subsumption_resolution,[],[f122,f128]) ).
fof(f203,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ transfinite_sequence(X1) ),
inference(forward_subsumption_resolution,[],[f202,f127]) ).
fof(f204,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| subset(relation_rng(X1),X0) ),
inference(forward_subsumption_resolution,[],[f203,f126]) ).
fof(f246,plain,
transfinite_sequence(sK17),
inference(resolution,[],[f126,f194]) ).
fof(f248,plain,
function(sK17),
inference(resolution,[],[f127,f194]) ).
fof(f250,plain,
relation(sK17),
inference(resolution,[],[f128,f194]) ).
fof(f397,plain,
subset(relation_rng(sK17),sK16),
inference(resolution,[],[f204,f194]) ).
fof(f517,plain,
! [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(sK17))
| transfinite_sequence_of(X0,sK16) ),
inference(resolution,[],[f193,f397]) ).
fof(f547,plain,
! [X0] :
( ~ relation(sK17)
| ~ function(sK17)
| transfinite_sequence_of(tseq_dom_restriction(sK17,X0),relation_rng(sK17))
| ~ ordinal(X0) ),
inference(resolution,[],[f124,f246]) ).
fof(f550,plain,
! [X0] :
( ~ function(sK17)
| transfinite_sequence_of(tseq_dom_restriction(sK17,X0),relation_rng(sK17))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f547,f250]) ).
fof(f553,plain,
! [X0] :
( ~ ordinal(X0)
| transfinite_sequence_of(tseq_dom_restriction(sK17,X0),relation_rng(sK17)) ),
inference(forward_subsumption_resolution,[],[f550,f248]) ).
fof(f791,plain,
transfinite_sequence_of(tseq_dom_restriction(sK17,sK18),relation_rng(sK17)),
inference(resolution,[],[f553,f195]) ).
fof(f983,plain,
transfinite_sequence_of(tseq_dom_restriction(sK17,sK18),sK16),
inference(resolution,[],[f791,f517]) ).
fof(f988,plain,
$false,
inference(forward_subsumption_resolution,[],[f983,f196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM412+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 19:51:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.17/0.47 % (3169504)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3169513)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4151461682:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (3169510)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3169509)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=929011906_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (3169510)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4116993139:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (3169511)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=643175764:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3169514)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=29963684:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (3169512)dis+10_1_sil=32000:sp=arity:random_seed=1474667522:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (3169515)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1546312227:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (3169514) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3169504-3169514"...
% 0.17/0.47 % (3169512) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3169504-3169512"...
% 0.17/0.47 % (3169514)...printing done.
% 0.17/0.47 % (3169510) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3169504-3169510"...
% 0.17/0.47 % (3169512)...printing done.
% 0.17/0.47 % (3169514)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 % (3169514)------------------------------
% 0.17/0.47 % (3169514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3169514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3169514)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3169514)Termination reason: Refutation
% 0.17/0.47 % (3169514)Time elapsed: 0.012 s
% 0.17/0.47 % (3169514)Peak memory usage: 12 MB
% 0.17/0.47 % (3169514)Instructions burned: 16 (million)
% 0.17/0.47 % (3169504)Success in time 0.046 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------