%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM412+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 : n013.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 12:15:05 PM UTC 2026
% Result : Theorem 3.59s 1.46s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 5 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 144 ( 64 ~; 54 |; 14 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f126,plain,
! [X0,X1] :
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f127,plain,
! [X0,X1] :
( function(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f128,plain,
! [X0,X1] :
( relation(X1)
| ~ transfinite_sequence_of(X1,X0) ),
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] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ),
inference(forward_subsumption_resolution,[],[f203,f126]) ).
fof(f205,plain,
! [X2,X0,X1] :
( transfinite_sequence_of(X2,X1)
| ~ transfinite_sequence_of(X2,relation_rng(X0))
| ~ transfinite_sequence_of(X0,X1) ),
inference(resolution,[],[f204,f193]) ).
fof(f282,plain,
! [X0] :
( ~ transfinite_sequence_of(tseq_dom_restriction(sK17,sK18),relation_rng(X0))
| ~ transfinite_sequence_of(X0,sK16) ),
inference(resolution,[],[f205,f196]) ).
fof(f283,plain,
( ~ transfinite_sequence_of(sK17,sK16)
| ~ relation(sK17)
| ~ function(sK17)
| ~ transfinite_sequence(sK17)
| ~ ordinal(sK18) ),
inference(resolution,[],[f282,f124]) ).
fof(f294,plain,
( ~ transfinite_sequence_of(sK17,sK16)
| ~ function(sK17)
| ~ transfinite_sequence(sK17)
| ~ ordinal(sK18) ),
inference(forward_subsumption_resolution,[],[f283,f128]) ).
fof(f295,plain,
( ~ transfinite_sequence_of(sK17,sK16)
| ~ transfinite_sequence(sK17)
| ~ ordinal(sK18) ),
inference(forward_subsumption_resolution,[],[f294,f127]) ).
fof(f296,plain,
( ~ transfinite_sequence_of(sK17,sK16)
| ~ ordinal(sK18) ),
inference(forward_subsumption_resolution,[],[f295,f126]) ).
fof(f297,plain,
~ ordinal(sK18),
inference(forward_subsumption_resolution,[],[f296,f194]) ).
fof(f298,plain,
$false,
inference(forward_subsumption_resolution,[],[f297,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM412+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.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
% 0.10/0.37 % DateTime : Sun Sep 27 19:48:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.59/1.46 % (512366)Detected formulas, will run a generic FOF schedule.
% 3.59/1.46 % (512375)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3814330385:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/1.46 % (512375)Refutation not found, incomplete strategy
% 3.59/1.46 % (512375)------------------------------
% 3.59/1.46 % (512375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (512375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (512375)CaDiCaL version: 2.1.3
% 3.59/1.46 % (512375)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.46 % (512375)Time elapsed: 0.001 s
% 3.59/1.46 % (512375)Peak memory usage: 88 MB
% 3.59/1.46 % (512375)Instructions burned: 2 (million)
% 3.59/1.46 % (512373)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=3387942569:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/1.46 % (512372)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=2376698441:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/1.46 % (512371)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=3044279022:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/1.46 % (512374)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1363103507:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/1.46 % (512374)Refutation not found, incomplete strategy
% 3.59/1.46 % (512374)------------------------------
% 3.59/1.46 % (512374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (512374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (512374)CaDiCaL version: 2.1.3
% 3.59/1.46 % (512374)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.46 % (512374)Time elapsed: 0.001 s
% 3.59/1.46 % (512374)Peak memory usage: 87 MB
% 3.59/1.46 % (512376)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1606675289:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/1.46 % (512377)dis-21_1_sil=8000:lcm=predicate:random_seed=3589848816: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)
% 3.59/1.46 % (512376)First to succeed.
% 3.59/1.46 % (512376)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-512366"
% 3.59/1.46 % (512377)Instruction limit reached!
% 3.59/1.46 % (512377)------------------------------
% 3.59/1.46 % (512377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (512377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (512377)CaDiCaL version: 2.1.3
% 3.59/1.46 % (512377)Termination reason: Instruction limit
% 3.59/1.46 % (512377)Termination phase: Saturation
% 3.59/1.46 % (512377)Time elapsed: 0.071 s
% 3.59/1.46 % (512377)Peak memory usage: 89 MB
% 3.59/1.46 % (512377)Instructions burned: 130 (million)
% 3.59/1.46 % (512375)------------------------------
% 3.59/1.46 % (512375)------------------------------
% 3.59/1.46 % (512385)lrs+10_1_sil=8000:sp=occurrence:random_seed=2215611786:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.59/1.46 % (512385)Also succeeded, but the first one will report.
% 3.59/1.46 % (512386)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3393899002:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.59/1.46 % (512386)Also succeeded, but the first one will report.
% 3.59/1.46 % (512374)------------------------------
% 3.59/1.46 % (512374)------------------------------
% 3.59/1.46 % (512376)Refutation found. Thanks to Tanya!
% 3.59/1.46 % SZS status Theorem for theBenchmark
% 3.59/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.46 % (512376)------------------------------
% 3.59/1.46 % (512376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (512376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (512376)CaDiCaL version: 2.1.3
% 3.59/1.46 % (512376)Termination reason: Refutation
% 3.59/1.46 % (512376)Time elapsed: 0.006 s
% 3.59/1.46 % (512376)Peak memory usage: 89 MB
% 3.59/1.46 % (512376)Instructions burned: 6 (million)
% 3.59/1.46 % (512376)------------------------------
% 3.59/1.46 % (512376)------------------------------
% 3.59/1.46 % (512366)Success in time 0.427 s
% 3.59/1.46 % Vampire exiting
%------------------------------------------------------------------------------