TSTP Solution File: SET617+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -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 : Sun May 5 09:14:29 EDT 2024
% Result : Theorem 0.10s 0.34s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 77 ( 25 unt; 0 def)
% Number of atoms : 168 ( 53 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 66 ~; 56 |; 15 &)
% ( 17 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 71 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f132,plain,
$false,
inference(avatar_sat_refutation,[],[f57,f61,f70,f79,f84,f88,f92,f96,f99,f105,f115,f119,f126,f130,f131]) ).
fof(f131,plain,
( ~ spl3_6
| spl3_5
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f108,f103,f76,f81]) ).
fof(f81,plain,
( spl3_6
<=> sK0 = union(sK0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f76,plain,
( spl3_5
<=> sK0 = union(empty_set,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f103,plain,
( spl3_10
<=> ! [X0,X1] : union(X0,X1) = union(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f108,plain,
( sK0 != union(sK0,empty_set)
| spl3_5
| ~ spl3_10 ),
inference(superposition,[],[f78,f104]) ).
fof(f104,plain,
( ! [X0,X1] : union(X0,X1) = union(X1,X0)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f78,plain,
( sK0 != union(empty_set,sK0)
| spl3_5 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f130,plain,
spl3_14,
inference(avatar_split_clause,[],[f45,f128]) ).
fof(f128,plain,
( spl3_14
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f45,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f26,f27]) ).
fof(f27,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f126,plain,
spl3_13,
inference(avatar_split_clause,[],[f40,f124]) ).
fof(f124,plain,
( spl3_13
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f40,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f119,plain,
spl3_12,
inference(avatar_split_clause,[],[f47,f117]) ).
fof(f117,plain,
( spl3_12
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f115,plain,
spl3_11,
inference(avatar_split_clause,[],[f46,f113]) ).
fof(f113,plain,
( spl3_11
<=> ! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f105,plain,
spl3_10,
inference(avatar_split_clause,[],[f35,f103]) ).
fof(f35,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f99,plain,
( spl3_6
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f98,plain,
( $false
| spl3_6
| ~ spl3_8 ),
inference(trivial_inequality_removal,[],[f97]) ).
fof(f97,plain,
( sK0 != sK0
| spl3_6
| ~ spl3_8 ),
inference(superposition,[],[f83,f91]) ).
fof(f91,plain,
( ! [X0] : union(X0,empty_set) = X0
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f90,plain,
( spl3_8
<=> ! [X0] : union(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f83,plain,
( sK0 != union(sK0,empty_set)
| spl3_6 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f96,plain,
spl3_9,
inference(avatar_split_clause,[],[f34,f94]) ).
fof(f94,plain,
( spl3_9
<=> ! [X0] : difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f34,plain,
! [X0] : difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
fof(f92,plain,
spl3_8,
inference(avatar_split_clause,[],[f33,f90]) ).
fof(f33,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).
fof(f88,plain,
spl3_7,
inference(avatar_split_clause,[],[f32,f86]) ).
fof(f86,plain,
( spl3_7
<=> ! [X0] : empty_set = difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f32,plain,
! [X0] : empty_set = difference(empty_set,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : empty_set = difference(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
fof(f84,plain,
( ~ spl3_6
| spl3_3 ),
inference(avatar_split_clause,[],[f74,f63,f81]) ).
fof(f63,plain,
( spl3_3
<=> sK0 = union(difference(sK0,empty_set),difference(empty_set,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f74,plain,
( sK0 != union(sK0,empty_set)
| spl3_3 ),
inference(forward_demodulation,[],[f73,f34]) ).
fof(f73,plain,
( sK0 != union(difference(sK0,empty_set),empty_set)
| spl3_3 ),
inference(forward_demodulation,[],[f65,f32]) ).
fof(f65,plain,
( sK0 != union(difference(sK0,empty_set),difference(empty_set,sK0))
| spl3_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f79,plain,
( ~ spl3_5
| spl3_4 ),
inference(avatar_split_clause,[],[f72,f67,f76]) ).
fof(f67,plain,
( spl3_4
<=> sK0 = union(difference(empty_set,sK0),difference(sK0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f72,plain,
( sK0 != union(empty_set,sK0)
| spl3_4 ),
inference(forward_demodulation,[],[f71,f32]) ).
fof(f71,plain,
( sK0 != union(difference(empty_set,sK0),sK0)
| spl3_4 ),
inference(forward_demodulation,[],[f69,f34]) ).
fof(f69,plain,
( sK0 != union(difference(empty_set,sK0),difference(sK0,empty_set))
| spl3_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f48,f67,f63]) ).
fof(f48,plain,
( sK0 != union(difference(empty_set,sK0),difference(sK0,empty_set))
| sK0 != union(difference(sK0,empty_set),difference(empty_set,sK0)) ),
inference(definition_unfolding,[],[f29,f37,f37]) ).
fof(f37,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f29,plain,
( sK0 != symmetric_difference(empty_set,sK0)
| sK0 != symmetric_difference(sK0,empty_set) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( sK0 != symmetric_difference(empty_set,sK0)
| sK0 != symmetric_difference(sK0,empty_set) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f17]) ).
fof(f17,plain,
( ? [X0] :
( symmetric_difference(empty_set,X0) != X0
| symmetric_difference(X0,empty_set) != X0 )
=> ( sK0 != symmetric_difference(empty_set,sK0)
| sK0 != symmetric_difference(sK0,empty_set) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0] :
( symmetric_difference(empty_set,X0) != X0
| symmetric_difference(X0,empty_set) != X0 ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0] :
( symmetric_difference(empty_set,X0) = X0
& symmetric_difference(X0,empty_set) = X0 ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0] :
( symmetric_difference(empty_set,X0) = X0
& symmetric_difference(X0,empty_set) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th92) ).
fof(f61,plain,
spl3_2,
inference(avatar_split_clause,[],[f31,f59]) ).
fof(f59,plain,
( spl3_2
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f31,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f57,plain,
spl3_1,
inference(avatar_split_clause,[],[f30,f55]) ).
fof(f55,plain,
( spl3_1
<=> ! [X0] : ~ member(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f30,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 16:36:08 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.32 % (25179)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33 % (25182)WARNING: value z3 for option sas not known
% 0.10/0.33 % (25182)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)
% 0.10/0.33 % (25181)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.33 % (25183)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.33 % (25180)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.33 % (25184)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)
% 0.10/0.33 % (25185)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)
% 0.10/0.33 % (25186)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)
% 0.10/0.33 TRYING [1]
% 0.10/0.33 TRYING [2]
% 0.10/0.33 % (25184)First to succeed.
% 0.10/0.33 % (25185)Also succeeded, but the first one will report.
% 0.10/0.33 TRYING [3]
% 0.10/0.33 % (25186)Also succeeded, but the first one will report.
% 0.10/0.33 % (25182)Also succeeded, but the first one will report.
% 0.10/0.33 TRYING [1]
% 0.10/0.33 % (25184)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25179"
% 0.10/0.33 TRYING [1]
% 0.10/0.33 TRYING [2]
% 0.10/0.34 % (25184)Refutation found. Thanks to Tanya!
% 0.10/0.34 % SZS status Theorem for theBenchmark
% 0.10/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.34 % (25184)------------------------------
% 0.10/0.34 % (25184)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.34 % (25184)Termination reason: Refutation
% 0.10/0.34
% 0.10/0.34 % (25184)Memory used [KB]: 839
% 0.10/0.34 % (25184)Time elapsed: 0.005 s
% 0.10/0.34 % (25184)Instructions burned: 6 (million)
% 0.10/0.34 % (25179)Success in time 0.019 s
%------------------------------------------------------------------------------