TSTP Solution File: NUM412+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:22:00 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 7 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 195 ( 90 ~; 71 |; 20 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 62 ( 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f427,plain,
$false,
inference(resolution,[],[f425,f238]) ).
fof(f238,plain,
relation(sK1),
inference(resolution,[],[f167,f129]) ).
fof(f129,plain,
transfinite_sequence_of(sK1,sK0),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
( ~ transfinite_sequence_of(tseq_dom_restriction(sK1,sK2),sK0)
& ordinal(sK2)
& transfinite_sequence_of(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f57,f93,f92]) ).
fof(f92,plain,
( ? [X0,X1] :
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0)
& ordinal(X2) )
& transfinite_sequence_of(X1,X0) )
=> ( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(sK1,X2),sK0)
& ordinal(X2) )
& transfinite_sequence_of(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(sK1,X2),sK0)
& ordinal(X2) )
=> ( ~ transfinite_sequence_of(tseq_dom_restriction(sK1,sK2),sK0)
& ordinal(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f57,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(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,[],[f43]) ).
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(f167,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| relation(X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( transfinite_sequence(X1)
& function(X1)
& relation(X1) )
| ~ transfinite_sequence_of(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ( transfinite_sequence(X1)
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f425,plain,
~ relation(sK1),
inference(resolution,[],[f422,f240]) ).
fof(f240,plain,
function(sK1),
inference(resolution,[],[f168,f129]) ).
fof(f168,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| function(X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f422,plain,
( ~ function(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f420,f130]) ).
fof(f130,plain,
ordinal(sK2),
inference(cnf_transformation,[],[f94]) ).
fof(f420,plain,
( ~ ordinal(sK2)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f415,f129]) ).
fof(f415,plain,
! [X0] :
( ~ transfinite_sequence_of(sK1,X0)
| ~ relation(sK1)
| ~ function(sK1)
| ~ ordinal(sK2) ),
inference(resolution,[],[f406,f129]) ).
fof(f406,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(sK1,X1)
| ~ transfinite_sequence_of(sK1,X0)
| ~ relation(sK1)
| ~ function(sK1)
| ~ ordinal(sK2) ),
inference(resolution,[],[f405,f129]) ).
fof(f405,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(sK1,sK0)
| ~ transfinite_sequence_of(sK1,X1)
| ~ transfinite_sequence_of(sK1,X0)
| ~ relation(sK1)
| ~ function(sK1)
| ~ ordinal(sK2) ),
inference(resolution,[],[f404,f169]) ).
fof(f169,plain,
! [X0,X1] :
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f404,plain,
! [X0] :
( ~ transfinite_sequence(sK1)
| ~ ordinal(sK2)
| ~ function(sK1)
| ~ relation(sK1)
| ~ transfinite_sequence_of(sK1,X0)
| ~ transfinite_sequence_of(sK1,sK0) ),
inference(duplicate_literal_removal,[],[f399]) ).
fof(f399,plain,
! [X0] :
( ~ ordinal(sK2)
| ~ transfinite_sequence(sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ transfinite_sequence_of(sK1,X0)
| ~ relation(sK1)
| ~ function(sK1)
| ~ transfinite_sequence_of(sK1,sK0) ),
inference(resolution,[],[f172,f344]) ).
fof(f344,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(tseq_dom_restriction(sK1,sK2),relation_rng(X0))
| ~ transfinite_sequence_of(X0,X1)
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence_of(X0,sK0) ),
inference(resolution,[],[f336,f169]) ).
fof(f336,plain,
! [X0] :
( ~ transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ transfinite_sequence_of(tseq_dom_restriction(sK1,sK2),relation_rng(X0)) ),
inference(resolution,[],[f174,f273]) ).
fof(f273,plain,
! [X0] :
( ~ subset(X0,sK0)
| ~ transfinite_sequence_of(tseq_dom_restriction(sK1,sK2),X0) ),
inference(resolution,[],[f163,f131]) ).
fof(f131,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sK1,sK2),sK0),
inference(cnf_transformation,[],[f94]) ).
fof(f163,plain,
! [X2,X0,X1] :
( transfinite_sequence_of(X2,X1)
| ~ transfinite_sequence_of(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( transfinite_sequence_of(X2,X1)
| ~ transfinite_sequence_of(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
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(f174,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( ( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0) )
& ( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( ( transfinite_sequence(X1)
& function(X1)
& relation(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f172,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& transfinite_sequence(X0)
& function(X0)
& relation(X0) )
=> transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 23:42:29 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (16075)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (16078)WARNING: value z3 for option sas not known
% 0.15/0.39 % (16076)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (16077)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (16079)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (16080)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (16081)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (16078)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 % (16082)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.40 TRYING [4]
% 0.15/0.40 % (16081)First to succeed.
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.40 % (16081)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (16081)------------------------------
% 0.15/0.40 % (16081)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40 % (16081)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (16081)Memory used [KB]: 1003
% 0.15/0.40 % (16081)Time elapsed: 0.012 s
% 0.15/0.40 % (16081)Instructions burned: 18 (million)
% 0.15/0.40 % (16081)------------------------------
% 0.15/0.40 % (16081)------------------------------
% 0.15/0.40 % (16075)Success in time 0.019 s
%------------------------------------------------------------------------------