TSTP Solution File: NUM386+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : NUM386+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 : n027.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 17:59:19 EDT 2022
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 8 unt; 0 def)
% Number of atoms : 223 ( 71 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 274 ( 100 ~; 113 |; 47 &)
% ( 10 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 99 ( 82 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f186,plain,
$false,
inference(subsumption_resolution,[],[f181,f166]) ).
fof(f166,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f165]) ).
fof(f165,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f122]) ).
fof(f122,plain,
! [X2,X0,X1] :
( in(X2,X1)
| X0 != X2
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f78,f79]) ).
fof(f79,plain,
! [X0,X1] :
( ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) )
=> ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) ) ) ),
inference(rectify,[],[f77]) ).
fof(f77,plain,
! [X1,X0] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> X1 = X2 )
<=> singleton(X1) = X0 ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f181,plain,
~ in(sK2,singleton(sK2)),
inference(backward_demodulation,[],[f175,f180]) ).
fof(f180,plain,
sK3 = sK2,
inference(subsumption_resolution,[],[f179,f175]) ).
fof(f179,plain,
( sK3 = sK2
| in(sK3,singleton(sK2)) ),
inference(subsumption_resolution,[],[f177,f171]) ).
fof(f171,plain,
~ in(sK3,sK2),
inference(subsumption_resolution,[],[f162,f168]) ).
fof(f168,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X1,X0))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f144]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X1)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X1,X0) != X2 )
& ( set_union2(X1,X0) = X2
| ( ( ( ~ in(sK9(X0,X1,X2),X1)
& ~ in(sK9(X0,X1,X2),X0) )
| ~ in(sK9(X0,X1,X2),X2) )
& ( in(sK9(X0,X1,X2),X1)
| in(sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X2) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f92,f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| ~ in(X4,X2) )
& ( in(X4,X1)
| in(X4,X0)
| in(X4,X2) ) )
=> ( ( ( ~ in(sK9(X0,X1,X2),X1)
& ~ in(sK9(X0,X1,X2),X0) )
| ~ in(sK9(X0,X1,X2),X2) )
& ( in(sK9(X0,X1,X2),X1)
| in(sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X1,X0) != X2 )
& ( set_union2(X1,X0) = X2
| ? [X4] :
( ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| ~ in(X4,X2) )
& ( in(X4,X1)
| in(X4,X0)
| in(X4,X2) ) ) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X0,X2,X1] :
( ( ! [X3] :
( ( in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) )
& ( in(X3,X2)
| in(X3,X0)
| ~ in(X3,X1) ) )
| set_union2(X2,X0) != X1 )
& ( set_union2(X2,X0) = X1
| ? [X3] :
( ( ( ~ in(X3,X2)
& ~ in(X3,X0) )
| ~ in(X3,X1) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) ) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X2,X1] :
( ( ! [X3] :
( ( in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) )
& ( in(X3,X2)
| in(X3,X0)
| ~ in(X3,X1) ) )
| set_union2(X2,X0) != X1 )
& ( set_union2(X2,X0) = X1
| ? [X3] :
( ( ( ~ in(X3,X2)
& ~ in(X3,X0) )
| ~ in(X3,X1) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X2,X1] :
( ! [X3] :
( in(X3,X1)
<=> ( in(X3,X2)
| in(X3,X0) ) )
<=> set_union2(X2,X0) = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X2,X0] :
( ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) )
<=> set_union2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f162,plain,
( ~ in(sK3,sK2)
| ~ in(sK3,set_union2(sK2,singleton(sK2))) ),
inference(definition_unfolding,[],[f117,f124]) ).
fof(f124,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f117,plain,
( ~ in(sK3,succ(sK2))
| ~ in(sK3,sK2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ( ~ in(sK3,succ(sK2))
| ( ~ in(sK3,sK2)
& sK3 != sK2 ) )
& ( in(sK3,succ(sK2))
| in(sK3,sK2)
| sK3 = sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f72,f73]) ).
fof(f73,plain,
( ? [X0,X1] :
( ( ~ in(X1,succ(X0))
| ( ~ in(X1,X0)
& X0 != X1 ) )
& ( in(X1,succ(X0))
| in(X1,X0)
| X0 = X1 ) )
=> ( ( ~ in(sK3,succ(sK2))
| ( ~ in(sK3,sK2)
& sK3 != sK2 ) )
& ( in(sK3,succ(sK2))
| in(sK3,sK2)
| sK3 = sK2 ) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0,X1] :
( ( ~ in(X1,succ(X0))
| ( ~ in(X1,X0)
& X0 != X1 ) )
& ( in(X1,succ(X0))
| in(X1,X0)
| X0 = X1 ) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
? [X1,X0] :
( ( ~ in(X0,succ(X1))
| ( ~ in(X0,X1)
& X0 != X1 ) )
& ( in(X0,succ(X1))
| in(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
? [X1,X0] :
( ( ~ in(X0,succ(X1))
| ( ~ in(X0,X1)
& X0 != X1 ) )
& ( in(X0,succ(X1))
| in(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
? [X1,X0] :
( ( in(X0,X1)
| X0 = X1 )
<~> in(X0,succ(X1)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( in(X0,succ(X1))
<=> ( in(X0,X1)
| X0 = X1 ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0,X1] :
( in(X0,succ(X1))
<=> ( in(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(f177,plain,
( sK3 = sK2
| in(sK3,sK2)
| in(sK3,singleton(sK2)) ),
inference(resolution,[],[f172,f170]) ).
fof(f170,plain,
! [X3,X0,X1] :
( ~ in(X3,set_union2(X1,X0))
| in(X3,X0)
| in(X3,X1) ),
inference(equality_resolution,[],[f142]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f172,plain,
( in(sK3,set_union2(sK2,singleton(sK2)))
| sK3 = sK2 ),
inference(subsumption_resolution,[],[f164,f168]) ).
fof(f164,plain,
( in(sK3,set_union2(sK2,singleton(sK2)))
| in(sK3,sK2)
| sK3 = sK2 ),
inference(definition_unfolding,[],[f115,f124]) ).
fof(f115,plain,
( in(sK3,succ(sK2))
| in(sK3,sK2)
| sK3 = sK2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f175,plain,
~ in(sK3,singleton(sK2)),
inference(subsumption_resolution,[],[f174,f167]) ).
fof(f167,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f121]) ).
fof(f121,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f174,plain,
( sK3 != sK2
| ~ in(sK3,singleton(sK2)) ),
inference(resolution,[],[f163,f169]) ).
fof(f169,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X1,X0))
| ~ in(X3,X0) ),
inference(equality_resolution,[],[f143]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f163,plain,
( ~ in(sK3,set_union2(sK2,singleton(sK2)))
| sK3 != sK2 ),
inference(definition_unfolding,[],[f116,f124]) ).
fof(f116,plain,
( ~ in(sK3,succ(sK2))
| sK3 != sK2 ),
inference(cnf_transformation,[],[f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.30 % Computer : n027.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 30 18:50:46 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.15/0.45 % (30991)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.46 % (30994)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.46 % (30992)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.47 % (30991)Instruction limit reached!
% 0.15/0.47 % (30991)------------------------------
% 0.15/0.47 % (30991)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.47 % (30991)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.47 % (30991)Termination reason: Unknown
% 0.15/0.47 % (30991)Termination phase: Saturation
% 0.15/0.47
% 0.15/0.47 % (30991)Memory used [KB]: 6012
% 0.15/0.47 % (30991)Time elapsed: 0.005 s
% 0.15/0.47 % (30991)Instructions burned: 3 (million)
% 0.15/0.47 % (30991)------------------------------
% 0.15/0.47 % (30991)------------------------------
% 0.15/0.47 % (31010)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)
% 0.15/0.47 % (31002)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)
% 0.15/0.47 % (31003)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.48 % (30993)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.15/0.48 % (31011)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)
% 0.15/0.48 % (30994)First to succeed.
% 0.15/0.48 % (30994)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (30994)------------------------------
% 0.15/0.48 % (30994)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.48 % (30994)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.48 % (30994)Termination reason: Refutation
% 0.15/0.48
% 0.15/0.48 % (30994)Memory used [KB]: 1535
% 0.15/0.48 % (30994)Time elapsed: 0.122 s
% 0.15/0.48 % (30994)Instructions burned: 4 (million)
% 0.15/0.48 % (30994)------------------------------
% 0.15/0.48 % (30994)------------------------------
% 0.15/0.48 % (30988)Success in time 0.169 s
%------------------------------------------------------------------------------