TSTP Solution File: NUM414+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM414+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 May 21 01:57:22 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 120 ( 15 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 148 ( 64 ~; 36 |; 35 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 41 ( 33 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f730,plain,
$false,
inference(subsumption_resolution,[],[f729,f698]) ).
fof(f698,plain,
~ ordinal_subset(sK1,sK2),
inference(unit_resulting_resolution,[],[f124,f125,f586,f161]) ).
fof(f161,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f586,plain,
~ subset(sK1,sK2),
inference(unit_resulting_resolution,[],[f126,f127,f163]) ).
fof(f163,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f127,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ~ proper_subset(sK2,sK1)
& sK1 != sK2
& ~ proper_subset(sK1,sK2)
& ordinal(sK2)
& ordinal(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f58,f89,f88]) ).
fof(f88,plain,
( ? [X0] :
( ? [X1] :
( ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1)
& ordinal(X1) )
& ordinal(X0) )
=> ( ? [X1] :
( ~ proper_subset(X1,sK1)
& sK1 != X1
& ~ proper_subset(sK1,X1)
& ordinal(X1) )
& ordinal(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
( ? [X1] :
( ~ proper_subset(X1,sK1)
& sK1 != X1
& ~ proper_subset(sK1,X1)
& ordinal(X1) )
=> ( ~ proper_subset(sK2,sK1)
& sK1 != sK2
& ~ proper_subset(sK1,sK2)
& ordinal(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
? [X0] :
( ? [X1] :
( ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1)
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
? [X0] :
( ? [X1] :
( ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1)
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1) ) ) ),
inference(negated_conjecture,[],[f38]) ).
fof(f38,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ proper_subset(X1,X0)
& X0 != X1
& ~ proper_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_ordinal1) ).
fof(f126,plain,
~ proper_subset(sK1,sK2),
inference(cnf_transformation,[],[f90]) ).
fof(f125,plain,
ordinal(sK2),
inference(cnf_transformation,[],[f90]) ).
fof(f124,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f90]) ).
fof(f729,plain,
ordinal_subset(sK1,sK2),
inference(subsumption_resolution,[],[f728,f125]) ).
fof(f728,plain,
( ~ ordinal(sK2)
| ordinal_subset(sK1,sK2) ),
inference(subsumption_resolution,[],[f727,f124]) ).
fof(f727,plain,
( ~ ordinal(sK1)
| ~ ordinal(sK2)
| ordinal_subset(sK1,sK2) ),
inference(subsumption_resolution,[],[f709,f587]) ).
fof(f587,plain,
~ subset(sK2,sK1),
inference(unit_resulting_resolution,[],[f128,f127,f163]) ).
fof(f128,plain,
~ proper_subset(sK2,sK1),
inference(cnf_transformation,[],[f90]) ).
fof(f709,plain,
( subset(sK2,sK1)
| ~ ordinal(sK1)
| ~ ordinal(sK2)
| ordinal_subset(sK1,sK2) ),
inference(resolution,[],[f161,f613]) ).
fof(f613,plain,
( ordinal_subset(sK2,sK1)
| ordinal_subset(sK1,sK2) ),
inference(resolution,[],[f595,f125]) ).
fof(f595,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal_subset(sK1,X0)
| ordinal_subset(X0,sK1) ),
inference(resolution,[],[f160,f124]) ).
fof(f160,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM414+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 04:32:53 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (11145)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (11147)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (11152)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)
% 0.14/0.37 % (11150)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)
% 0.14/0.37 % (11152)First to succeed.
% 0.14/0.37 % (11152)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11145"
% 0.14/0.38 % (11152)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (11152)------------------------------
% 0.14/0.38 % (11152)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (11152)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (11152)Memory used [KB]: 934
% 0.14/0.38 % (11152)Time elapsed: 0.010 s
% 0.14/0.38 % (11152)Instructions burned: 15 (million)
% 0.14/0.38 % (11145)Success in time 0.026 s
%------------------------------------------------------------------------------