TSTP Solution File: SET633+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET633+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 : n016.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 Apr 30 15:08:58 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 64 ( 23 unt; 0 def)
% Number of atoms : 161 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 60 ~; 50 |; 26 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 107 ( 95 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f110,plain,
$false,
inference(avatar_sat_refutation,[],[f54,f59,f64,f68,f72,f76,f80,f84,f88,f96,f101,f105,f109]) ).
fof(f109,plain,
( ~ spl5_1
| ~ spl5_2
| spl5_3
| ~ spl5_11 ),
inference(avatar_split_clause,[],[f106,f99,f61,f56,f51]) ).
fof(f51,plain,
( spl5_1
<=> subset(difference(sK0,sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f56,plain,
( spl5_2
<=> subset(difference(sK1,sK0),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f61,plain,
( spl5_3
<=> subset(union(difference(sK0,sK1),difference(sK1,sK0)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f99,plain,
( spl5_11
<=> ! [X2,X0,X1] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f106,plain,
( ~ subset(difference(sK1,sK0),sK2)
| ~ subset(difference(sK0,sK1),sK2)
| spl5_3
| ~ spl5_11 ),
inference(resolution,[],[f100,f63]) ).
fof(f63,plain,
( ~ subset(union(difference(sK0,sK1),difference(sK1,sK0)),sK2)
| spl5_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f100,plain,
( ! [X2,X0,X1] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f105,plain,
spl5_12,
inference(avatar_split_clause,[],[f45,f103]) ).
fof(f103,plain,
( spl5_12
<=> ! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f45,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f101,plain,
spl5_11,
inference(avatar_split_clause,[],[f42,f99]) ).
fof(f42,plain,
! [X2,X0,X1] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_subset) ).
fof(f96,plain,
spl5_10,
inference(avatar_split_clause,[],[f39,f94]) ).
fof(f94,plain,
( spl5_10
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f39,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f23,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,[],[f22]) ).
fof(f22,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,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f88,plain,
spl5_9,
inference(avatar_split_clause,[],[f44,f86]) ).
fof(f86,plain,
( spl5_9
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f84,plain,
spl5_8,
inference(avatar_split_clause,[],[f43,f82]) ).
fof(f82,plain,
( spl5_8
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f80,plain,
spl5_7,
inference(avatar_split_clause,[],[f41,f78]) ).
fof(f78,plain,
( spl5_7
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f76,plain,
spl5_6,
inference(avatar_split_clause,[],[f40,f74]) ).
fof(f74,plain,
( spl5_6
<=> ! [X0,X1] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f72,plain,
spl5_5,
inference(avatar_split_clause,[],[f33,f70]) ).
fof(f70,plain,
( spl5_5
<=> ! [X0,X1] : union(X0,X1) = union(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f33,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f68,plain,
spl5_4,
inference(avatar_split_clause,[],[f31,f66]) ).
fof(f66,plain,
( spl5_4
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f31,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f64,plain,
~ spl5_3,
inference(avatar_split_clause,[],[f46,f61]) ).
fof(f46,plain,
~ subset(union(difference(sK0,sK1),difference(sK1,sK0)),sK2),
inference(definition_unfolding,[],[f30,f34]) ).
fof(f34,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(f30,plain,
~ subset(symmetric_difference(sK0,sK1),sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( ~ subset(symmetric_difference(sK0,sK1),sK2)
& subset(difference(sK1,sK0),sK2)
& subset(difference(sK0,sK1),sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f16]) ).
fof(f16,plain,
( ? [X0,X1,X2] :
( ~ subset(symmetric_difference(X0,X1),X2)
& subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) )
=> ( ~ subset(symmetric_difference(sK0,sK1),sK2)
& subset(difference(sK1,sK0),sK2)
& subset(difference(sK0,sK1),sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ~ subset(symmetric_difference(X0,X1),X2)
& subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ~ subset(symmetric_difference(X0,X1),X2)
& subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) )
=> subset(symmetric_difference(X0,X1),X2) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( ( subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) )
=> subset(symmetric_difference(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th115) ).
fof(f59,plain,
spl5_2,
inference(avatar_split_clause,[],[f29,f56]) ).
fof(f29,plain,
subset(difference(sK1,sK0),sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f54,plain,
spl5_1,
inference(avatar_split_clause,[],[f28,f51]) ).
fof(f28,plain,
subset(difference(sK0,sK1),sK2),
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 01:43:56 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (30597)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (30600)WARNING: value z3 for option sas not known
% 0.15/0.39 % (30599)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (30601)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (30600)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)
% 0.15/0.39 % (30602)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)
% 0.15/0.39 % (30605)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)
% 0.15/0.39 % (30604)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)
% 0.15/0.39 % (30598)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (30602)First to succeed.
% 0.15/0.40 TRYING [3]
% 0.22/0.40 % (30602)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (30602)------------------------------
% 0.22/0.40 % (30602)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40 % (30602)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (30602)Memory used [KB]: 780
% 0.22/0.40 % (30602)Time elapsed: 0.009 s
% 0.22/0.40 % (30602)Instructions burned: 5 (million)
% 0.22/0.40 % (30602)------------------------------
% 0.22/0.40 % (30602)------------------------------
% 0.22/0.40 % (30597)Success in time 0.035 s
%------------------------------------------------------------------------------