TSTP Solution File: SET162+4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET162+4 : 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 : n032.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 09:12:27 EDT 2024
% Result : Theorem 2.73s 0.74s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 43 ~; 41 |; 14 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 68 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8488,plain,
$false,
inference(avatar_sat_refutation,[],[f117,f1139,f8487]) ).
fof(f8487,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f8481]) ).
fof(f8481,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f8471,f112]) ).
fof(f112,plain,
( ~ subset(union(sK0,empty_set),sK0)
| spl4_1 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f110,plain,
( spl4_1
<=> subset(union(sK0,empty_set),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f8471,plain,
! [X0] : subset(union(X0,empty_set),X0),
inference(duplicate_literal_removal,[],[f8392]) ).
fof(f8392,plain,
! [X0] :
( subset(union(X0,empty_set),X0)
| subset(union(X0,empty_set),X0) ),
inference(resolution,[],[f4448,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f32,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f32,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,[],[f31]) ).
fof(f31,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,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f4448,plain,
! [X0,X1] :
( member(sK1(union(X0,empty_set),X1),X0)
| subset(union(X0,empty_set),X1) ),
inference(resolution,[],[f357,f54]) ).
fof(f54,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f357,plain,
! [X2,X0,X1] :
( member(sK1(union(X0,X1),X2),X1)
| member(sK1(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[],[f78,f56]) ).
fof(f56,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f1139,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f1138]) ).
fof(f1138,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f1124,f116]) ).
fof(f116,plain,
( ~ subset(sK0,union(sK0,empty_set))
| spl4_2 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f114,plain,
( spl4_2
<=> subset(sK0,union(sK0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f1124,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(duplicate_literal_removal,[],[f1085]) ).
fof(f1085,plain,
! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[],[f96,f56]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ member(sK1(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f79,f57]) ).
fof(f79,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f117,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f108,f114,f110]) ).
fof(f108,plain,
( ~ subset(sK0,union(sK0,empty_set))
| ~ subset(union(sK0,empty_set),sK0) ),
inference(resolution,[],[f58,f53]) ).
fof(f53,plain,
~ equal_set(union(sK0,empty_set),sK0),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
~ equal_set(union(sK0,empty_set),sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f29]) ).
fof(f29,plain,
( ? [X0] : ~ equal_set(union(X0,empty_set),X0)
=> ~ equal_set(union(sK0,empty_set),sK0) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
? [X0] : ~ equal_set(union(X0,empty_set),X0),
inference(ennf_transformation,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(union(X0,empty_set),X0),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0] : equal_set(union(X0,empty_set),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI18) ).
fof(f58,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET162+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n032.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 17:06:07 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.31 % (23361)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33 % (23364)WARNING: value z3 for option sas not known
% 0.16/0.33 % (23367)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)
% 0.16/0.33 % (23365)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33 % (23363)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33 % (23362)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33 % (23366)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)
% 0.16/0.33 % (23364)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)
% 0.16/0.33 % (23368)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)
% 0.16/0.33 TRYING [1]
% 0.16/0.33 TRYING [2]
% 0.16/0.33 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 TRYING [4]
% 0.16/0.35 TRYING [3]
% 0.16/0.35 TRYING [5]
% 0.16/0.36 TRYING [6]
% 0.16/0.37 TRYING [4]
% 0.16/0.40 TRYING [7]
% 0.16/0.41 TRYING [5]
% 0.16/0.46 TRYING [8]
% 0.16/0.53 TRYING [6]
% 2.04/0.60 TRYING [9]
% 2.73/0.74 % (23364)First to succeed.
% 2.73/0.74 % (23364)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23361"
% 2.73/0.74 % (23364)Refutation found. Thanks to Tanya!
% 2.73/0.74 % SZS status Theorem for theBenchmark
% 2.73/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/0.74 % (23364)------------------------------
% 2.73/0.74 % (23364)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.73/0.74 % (23364)Termination reason: Refutation
% 2.73/0.74
% 2.73/0.74 % (23364)Memory used [KB]: 15320
% 2.73/0.74 % (23364)Time elapsed: 0.411 s
% 2.73/0.74 % (23364)Instructions burned: 800 (million)
% 2.73/0.74 % (23361)Success in time 0.417 s
%------------------------------------------------------------------------------