TSTP Solution File: SET900+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET900+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 : n028.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 : Sun May 5 09:19:38 EDT 2024
% Result : Theorem 0.13s 0.36s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 25
% Syntax : Number of formulae : 73 ( 20 unt; 0 def)
% Number of atoms : 198 ( 80 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 223 ( 98 ~; 84 |; 21 &)
% ( 15 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 16 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 58 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f106,plain,
$false,
inference(avatar_sat_refutation,[],[f32,f37,f41,f46,f51,f56,f60,f64,f68,f74,f82,f92,f98,f104,f105]) ).
fof(f105,plain,
( spl5_2
| ~ spl5_14 ),
inference(avatar_split_clause,[],[f99,f96,f34]) ).
fof(f34,plain,
( spl5_2
<=> sK0 = singleton(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f96,plain,
( spl5_14
<=> ! [X0] :
( sK1 != X0
| sK0 = singleton(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f99,plain,
( sK0 = singleton(sK1)
| ~ spl5_14 ),
inference(equality_resolution,[],[f97]) ).
fof(f97,plain,
( ! [X0] :
( sK1 != X0
| sK0 = singleton(X0) )
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f104,plain,
( ~ spl5_15
| ~ spl5_7
| ~ spl5_13 ),
inference(avatar_split_clause,[],[f94,f89,f58,f101]) ).
fof(f101,plain,
( spl5_15
<=> in(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
fof(f58,plain,
( spl5_7
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f89,plain,
( spl5_13
<=> in(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f94,plain,
( ~ in(sK0,sK1)
| ~ spl5_7
| ~ spl5_13 ),
inference(resolution,[],[f91,f59]) ).
fof(f59,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f91,plain,
( in(sK1,sK0)
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f98,plain,
( spl5_1
| spl5_14
| ~ spl5_9
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f78,f72,f66,f96,f29]) ).
fof(f29,plain,
( spl5_1
<=> empty_set = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f66,plain,
( spl5_9
<=> ! [X0,X1] :
( sK2(X0,X1) != X1
| empty_set = X0
| singleton(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f72,plain,
( spl5_10
<=> ! [X0] :
( sK0 = singleton(X0)
| sK1 = sK2(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f78,plain,
( ! [X0] :
( sK1 != X0
| empty_set = sK0
| sK0 = singleton(X0) )
| ~ spl5_9
| ~ spl5_10 ),
inference(duplicate_literal_removal,[],[f75]) ).
fof(f75,plain,
( ! [X0] :
( sK1 != X0
| empty_set = sK0
| sK0 = singleton(X0)
| sK0 = singleton(X0) )
| ~ spl5_9
| ~ spl5_10 ),
inference(superposition,[],[f67,f73]) ).
fof(f73,plain,
( ! [X0] :
( sK1 = sK2(sK0,X0)
| sK0 = singleton(X0) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f67,plain,
( ! [X0,X1] :
( sK2(X0,X1) != X1
| empty_set = X0
| singleton(X1) = X0 )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f92,plain,
( spl5_12
| spl5_1
| spl5_13
| ~ spl5_8
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f77,f72,f62,f89,f29,f86]) ).
fof(f86,plain,
( spl5_12
<=> ! [X0] : sK0 = singleton(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f62,plain,
( spl5_8
<=> ! [X0,X1] :
( in(sK2(X0,X1),X0)
| empty_set = X0
| singleton(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f77,plain,
( ! [X0] :
( in(sK1,sK0)
| empty_set = sK0
| sK0 = singleton(X0) )
| ~ spl5_8
| ~ spl5_10 ),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f76,plain,
( ! [X0] :
( in(sK1,sK0)
| empty_set = sK0
| sK0 = singleton(X0)
| sK0 = singleton(X0) )
| ~ spl5_8
| ~ spl5_10 ),
inference(superposition,[],[f63,f73]) ).
fof(f63,plain,
( ! [X0,X1] :
( in(sK2(X0,X1),X0)
| empty_set = X0
| singleton(X1) = X0 )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f82,plain,
( spl5_11
| ~ spl5_7
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f70,f62,f58,f80]) ).
fof(f80,plain,
( spl5_11
<=> ! [X0,X1] :
( empty_set = X0
| singleton(X1) = X0
| ~ in(X0,sK2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f70,plain,
( ! [X0,X1] :
( empty_set = X0
| singleton(X1) = X0
| ~ in(X0,sK2(X0,X1)) )
| ~ spl5_7
| ~ spl5_8 ),
inference(resolution,[],[f63,f59]) ).
fof(f74,plain,
( spl5_10
| spl5_1
| ~ spl5_3
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f69,f62,f39,f29,f72]) ).
fof(f39,plain,
( spl5_3
<=> ! [X2] :
( sK1 = X2
| ~ in(X2,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f69,plain,
( ! [X0] :
( empty_set = sK0
| sK0 = singleton(X0)
| sK1 = sK2(sK0,X0) )
| ~ spl5_3
| ~ spl5_8 ),
inference(resolution,[],[f63,f40]) ).
fof(f40,plain,
( ! [X2] :
( ~ in(X2,sK0)
| sK1 = X2 )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f68,plain,
spl5_9,
inference(avatar_split_clause,[],[f25,f66]) ).
fof(f25,plain,
! [X0,X1] :
( sK2(X0,X1) != X1
| empty_set = X0
| singleton(X1) = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ( sK2(X0,X1) != X1
& in(sK2(X0,X1),X0) )
| empty_set = X0
| singleton(X1) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f10,f13]) ).
fof(f13,plain,
! [X0,X1] :
( ? [X2] :
( X1 != X2
& in(X2,X0) )
=> ( sK2(X0,X1) != X1
& in(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
! [X0,X1] :
( ? [X2] :
( X1 != X2
& in(X2,X0) )
| empty_set = X0
| singleton(X1) = X0 ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
~ ( ! [X2] :
~ ( X1 != X2
& in(X2,X0) )
& empty_set != X0
& singleton(X1) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_zfmisc_1) ).
fof(f64,plain,
spl5_8,
inference(avatar_split_clause,[],[f24,f62]) ).
fof(f24,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| empty_set = X0
| singleton(X1) = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f60,plain,
spl5_7,
inference(avatar_split_clause,[],[f23,f58]) ).
fof(f23,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f56,plain,
spl5_6,
inference(avatar_split_clause,[],[f27,f53]) ).
fof(f53,plain,
( spl5_6
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f27,plain,
empty(sK4),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
empty(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f3,f17]) ).
fof(f17,plain,
( ? [X0] : empty(X0)
=> empty(sK4) ),
introduced(choice_axiom,[]) ).
fof(f3,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f51,plain,
~ spl5_5,
inference(avatar_split_clause,[],[f26,f48]) ).
fof(f48,plain,
( spl5_5
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f26,plain,
~ empty(sK3),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
~ empty(sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f4,f15]) ).
fof(f15,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK3) ),
introduced(choice_axiom,[]) ).
fof(f4,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f46,plain,
spl5_4,
inference(avatar_split_clause,[],[f22,f43]) ).
fof(f43,plain,
( spl5_4
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f22,plain,
empty(empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f41,plain,
spl5_3,
inference(avatar_split_clause,[],[f21,f39]) ).
fof(f21,plain,
! [X2] :
( sK1 = X2
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
( ! [X2] :
( sK1 = X2
| ~ in(X2,sK0) )
& empty_set != sK0
& sK0 != singleton(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f11]) ).
fof(f11,plain,
( ? [X0,X1] :
( ! [X2] :
( X1 = X2
| ~ in(X2,X0) )
& empty_set != X0
& singleton(X1) != X0 )
=> ( ! [X2] :
( sK1 = X2
| ~ in(X2,sK0) )
& empty_set != sK0
& sK0 != singleton(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f8,plain,
? [X0,X1] :
( ! [X2] :
( X1 = X2
| ~ in(X2,X0) )
& empty_set != X0
& singleton(X1) != X0 ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
~ ( ! [X2] :
~ ( X1 != X2
& in(X2,X0) )
& empty_set != X0
& singleton(X1) != X0 ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
! [X0,X1] :
~ ( ! [X2] :
~ ( X1 != X2
& in(X2,X0) )
& empty_set != X0
& singleton(X1) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
fof(f37,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f19,f34]) ).
fof(f19,plain,
sK0 != singleton(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f32,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f20,f29]) ).
fof(f20,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET900+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri May 3 16:27:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (8779)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35 % (8784)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)
% 0.13/0.35 % (8784)First to succeed.
% 0.13/0.36 % (8784)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8779"
% 0.13/0.36 % (8784)Refutation found. Thanks to Tanya!
% 0.13/0.36 % SZS status Theorem for theBenchmark
% 0.13/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.36 % (8784)------------------------------
% 0.13/0.36 % (8784)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.36 % (8784)Termination reason: Refutation
% 0.13/0.36
% 0.13/0.36 % (8784)Memory used [KB]: 781
% 0.13/0.36 % (8784)Time elapsed: 0.003 s
% 0.13/0.36 % (8784)Instructions burned: 5 (million)
% 0.13/0.36 % (8779)Success in time 0.014 s
%------------------------------------------------------------------------------