%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM411+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 0.12s 0.44s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 5 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 120 ( 51 ~; 47 |; 12 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 55 ( 52 !; 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] :
( transfinite_sequence_of(X1,X0)
=> ( relation(X1)
& function(X1)
& transfinite_sequence(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f38,conjecture,
! [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(f39,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( transfinite_sequence_of(X2,X0)
=> transfinite_sequence_of(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f65,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(f66,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ( relation(X1)
& function(X1)
& transfinite_sequence(X1) )
| ~ transfinite_sequence_of(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f72,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f73,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
? [X0,X1] :
( ? [X2] :
( ~ transfinite_sequence_of(X2,X1)
& transfinite_sequence_of(X2,X0) )
& subset(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f83,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,[],[f66]) ).
fof(f101,plain,
( ~ transfinite_sequence_of(sK18,sK17)
& transfinite_sequence_of(sK18,sK16)
& subset(sK16,sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f76]) ).
fof(f113,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f114,plain,
! [X0,X1] :
( ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f115,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f116,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| function(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f117,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| relation(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f174,plain,
subset(sK16,sK17),
inference(cnf_transformation,[],[f101]) ).
fof(f175,plain,
transfinite_sequence_of(sK18,sK16),
inference(cnf_transformation,[],[f101]) ).
fof(f176,plain,
~ transfinite_sequence_of(sK18,sK17),
inference(cnf_transformation,[],[f101]) ).
fof(f256,plain,
! [X0] :
( ~ subset(X0,sK16)
| subset(X0,sK17) ),
inference(resolution,[],[f170,f174]) ).
fof(f263,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(forward_subsumption_resolution,[],[f113,f117]) ).
fof(f264,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ transfinite_sequence(X1) ),
inference(forward_subsumption_resolution,[],[f263,f116]) ).
fof(f265,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ),
inference(forward_subsumption_resolution,[],[f264,f115]) ).
fof(f273,plain,
! [X0] :
( subset(relation_rng(X0),sK17)
| ~ transfinite_sequence_of(X0,sK16) ),
inference(resolution,[],[f265,f256]) ).
fof(f276,plain,
! [X0] :
( transfinite_sequence_of(X0,sK17)
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,sK16) ),
inference(resolution,[],[f114,f273]) ).
fof(f278,plain,
! [X0] :
( transfinite_sequence_of(X0,sK17)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f276,f117]) ).
fof(f279,plain,
! [X0] :
( transfinite_sequence_of(X0,sK17)
| ~ transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f278,f116]) ).
fof(f280,plain,
! [X0] :
( ~ transfinite_sequence_of(X0,sK16)
| transfinite_sequence_of(X0,sK17) ),
inference(forward_subsumption_resolution,[],[f279,f115]) ).
fof(f281,plain,
transfinite_sequence_of(sK18,sK17),
inference(resolution,[],[f280,f175]) ).
fof(f283,plain,
$false,
inference(forward_subsumption_resolution,[],[f281,f176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.36 % Computer : n026.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 19:51:26 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 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
% 0.12/0.44 % (3169097)Will run a generic schedule for satisfiability detection.
% 0.12/0.44 % (3169105)dis+10_1_sil=32000:sp=arity:random_seed=1840686976:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.44 % (3169105) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3169097-3169105"...
% 0.12/0.44 % (3169105)...printing done.
% 0.12/0.44 % (3169105)Refutation found. Thanks to Tanya!
% 0.12/0.44 % SZS status Theorem for theBenchmark
% 0.12/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.44 % (3169105)------------------------------
% 0.12/0.44 % (3169105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.44 % (3169105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.44 % (3169105)CaDiCaL version: 2.1.3
% 0.12/0.44 % (3169105)Termination reason: Refutation
% 0.12/0.44 % (3169105)Time elapsed: 0.002 s
% 0.12/0.44 % (3169105)Peak memory usage: 12 MB
% 0.12/0.44 % (3169105)Instructions burned: 5 (million)
% 0.12/0.44 % (3169097)Success in time 0.026 s
% 0.12/0.44 % Vampire exiting
%------------------------------------------------------------------------------