TSTP Solution File: NUM414+1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n007.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 : Wed Aug 31 17:59:23 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 126 ( 17 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 154 ( 66 ~; 33 |; 38 &)
% ( 6 <=>; 11 =>; 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 : 48 ( 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f260,plain,
$false,
inference(subsumption_resolution,[],[f258,f250]) ).
fof(f250,plain,
~ ordinal_subset(sK7,sK8),
inference(subsumption_resolution,[],[f249,f184]) ).
fof(f184,plain,
ordinal(sK8),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
( ordinal(sK7)
& sK8 != sK7
& ~ proper_subset(sK7,sK8)
& ordinal(sK8)
& ~ proper_subset(sK8,sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f82,f115,f114]) ).
fof(f114,plain,
( ? [X0] :
( ordinal(X0)
& ? [X1] :
( X0 != X1
& ~ proper_subset(X0,X1)
& ordinal(X1)
& ~ proper_subset(X1,X0) ) )
=> ( ordinal(sK7)
& ? [X1] :
( sK7 != X1
& ~ proper_subset(sK7,X1)
& ordinal(X1)
& ~ proper_subset(X1,sK7) ) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
( ? [X1] :
( sK7 != X1
& ~ proper_subset(sK7,X1)
& ordinal(X1)
& ~ proper_subset(X1,sK7) )
=> ( sK8 != sK7
& ~ proper_subset(sK7,sK8)
& ordinal(sK8)
& ~ proper_subset(sK8,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( X0 != X1
& ~ proper_subset(X0,X1)
& ordinal(X1)
& ~ proper_subset(X1,X0) ) ),
inference(flattening,[],[f81]) ).
fof(f81,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(f249,plain,
( ~ ordinal_subset(sK7,sK8)
| ~ ordinal(sK8) ),
inference(subsumption_resolution,[],[f248,f187]) ).
fof(f187,plain,
ordinal(sK7),
inference(cnf_transformation,[],[f116]) ).
fof(f248,plain,
( ~ ordinal(sK7)
| ~ ordinal_subset(sK7,sK8)
| ~ ordinal(sK8) ),
inference(resolution,[],[f240,f171]) ).
fof(f171,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal_subset(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ( ( ordinal_subset(X1,X0)
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ~ ordinal_subset(X1,X0) ) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ( ordinal_subset(X1,X0)
<=> subset(X1,X0) )
| ~ ordinal(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( ordinal_subset(X1,X0)
<=> subset(X1,X0) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
<=> subset(X1,X0) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X1,X0] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( subset(X0,X1)
<=> ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f240,plain,
~ subset(sK7,sK8),
inference(unit_resulting_resolution,[],[f185,f186,f199]) ).
fof(f199,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X1,X0] :
( proper_subset(X1,X0)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X1,X0] :
( proper_subset(X1,X0)
| X0 = X1
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X1,X0] :
( ( X0 != X1
& subset(X1,X0) )
=> proper_subset(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f47,plain,
! [X1,X0] :
( proper_subset(X1,X0)
<=> ( X0 != X1
& subset(X1,X0) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X1,X0] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f186,plain,
sK8 != sK7,
inference(cnf_transformation,[],[f116]) ).
fof(f185,plain,
~ proper_subset(sK7,sK8),
inference(cnf_transformation,[],[f116]) ).
fof(f258,plain,
ordinal_subset(sK7,sK8),
inference(unit_resulting_resolution,[],[f187,f184,f242,f198]) ).
fof(f198,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ordinal_subset(X1,X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X1,X0] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X1,X0] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f242,plain,
~ ordinal_subset(sK8,sK7),
inference(unit_resulting_resolution,[],[f187,f184,f239,f171]) ).
fof(f239,plain,
~ subset(sK8,sK7),
inference(unit_resulting_resolution,[],[f183,f186,f199]) ).
fof(f183,plain,
~ proper_subset(sK8,sK7),
inference(cnf_transformation,[],[f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 06:14:30 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.50 % (828)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.51 % (835)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (835)Refutation not found, incomplete strategy% (835)------------------------------
% 0.20/0.51 % (835)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (843)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52 % (835)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (835)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52
% 0.20/0.52 % (835)Memory used [KB]: 6012
% 0.20/0.52 % (835)Time elapsed: 0.100 s
% 0.20/0.52 % (835)Instructions burned: 4 (million)
% 0.20/0.52 % (835)------------------------------
% 0.20/0.52 % (835)------------------------------
% 0.20/0.52 % (828)Refutation not found, incomplete strategy% (828)------------------------------
% 0.20/0.52 % (828)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (828)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (828)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52
% 0.20/0.52 % (828)Memory used [KB]: 5884
% 0.20/0.52 % (828)Time elapsed: 0.110 s
% 0.20/0.52 % (828)Instructions burned: 2 (million)
% 0.20/0.52 % (828)------------------------------
% 0.20/0.52 % (828)------------------------------
% 0.20/0.52 % (844)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.52 % (843)First to succeed.
% 0.20/0.53 % (843)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (843)------------------------------
% 0.20/0.53 % (843)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (843)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (843)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (843)Memory used [KB]: 6012
% 0.20/0.53 % (843)Time elapsed: 0.116 s
% 0.20/0.53 % (843)Instructions burned: 4 (million)
% 0.20/0.53 % (843)------------------------------
% 0.20/0.53 % (843)------------------------------
% 0.20/0.53 % (820)Success in time 0.169 s
%------------------------------------------------------------------------------