TSTP Solution File: SEU321+1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n006.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 18:28:44 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 179 ( 9 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 214 ( 79 ~; 62 |; 53 &)
% ( 2 <=>; 16 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 40 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f261,plain,
$false,
inference(subsumption_resolution,[],[f260,f147]) ).
fof(f147,plain,
~ empty_carrier(sK1),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( element(sK2,powerset(the_carrier(sK1)))
& element(sK3,the_carrier(sK1))
& ( ~ in(sK3,subset_complement(the_carrier(sK1),sK2))
| in(sK3,sK2) )
& ( in(sK3,subset_complement(the_carrier(sK1),sK2))
| ~ in(sK3,sK2) )
& ~ empty_carrier(sK1)
& one_sorted_str(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f109,f112,f111,f110]) ).
fof(f110,plain,
( ? [X0] :
( ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( ~ in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1) )
& ( in(X2,subset_complement(the_carrier(X0),X1))
| ~ in(X2,X1) ) ) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ? [X1] :
( element(X1,powerset(the_carrier(sK1)))
& ? [X2] :
( element(X2,the_carrier(sK1))
& ( ~ in(X2,subset_complement(the_carrier(sK1),X1))
| in(X2,X1) )
& ( in(X2,subset_complement(the_carrier(sK1),X1))
| ~ in(X2,X1) ) ) )
& ~ empty_carrier(sK1)
& one_sorted_str(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
( ? [X1] :
( element(X1,powerset(the_carrier(sK1)))
& ? [X2] :
( element(X2,the_carrier(sK1))
& ( ~ in(X2,subset_complement(the_carrier(sK1),X1))
| in(X2,X1) )
& ( in(X2,subset_complement(the_carrier(sK1),X1))
| ~ in(X2,X1) ) ) )
=> ( element(sK2,powerset(the_carrier(sK1)))
& ? [X2] :
( element(X2,the_carrier(sK1))
& ( ~ in(X2,subset_complement(the_carrier(sK1),sK2))
| in(X2,sK2) )
& ( in(X2,subset_complement(the_carrier(sK1),sK2))
| ~ in(X2,sK2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
( ? [X2] :
( element(X2,the_carrier(sK1))
& ( ~ in(X2,subset_complement(the_carrier(sK1),sK2))
| in(X2,sK2) )
& ( in(X2,subset_complement(the_carrier(sK1),sK2))
| ~ in(X2,sK2) ) )
=> ( element(sK3,the_carrier(sK1))
& ( ~ in(sK3,subset_complement(the_carrier(sK1),sK2))
| in(sK3,sK2) )
& ( in(sK3,subset_complement(the_carrier(sK1),sK2))
| ~ in(sK3,sK2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
? [X0] :
( ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( ~ in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1) )
& ( in(X2,subset_complement(the_carrier(X0),X1))
| ~ in(X2,X1) ) ) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
? [X0] :
( ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( ~ in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1) )
& ( in(X2,subset_complement(the_carrier(X0),X1))
| ~ in(X2,X1) ) ) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(nnf_transformation,[],[f89]) ).
fof(f89,plain,
? [X0] :
( ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( ~ in(X2,X1)
<~> in(X2,subset_complement(the_carrier(X0),X1)) ) ) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
? [X0] :
( ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( ~ in(X2,X1)
<~> in(X2,subset_complement(the_carrier(X0),X1)) ) ) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ~ in(X2,X1)
<=> in(X2,subset_complement(the_carrier(X0),X1)) ) ) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f40,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ~ in(X2,X1)
<=> in(X2,subset_complement(the_carrier(X0),X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f260,plain,
empty_carrier(sK1),
inference(subsumption_resolution,[],[f259,f182]) ).
fof(f182,plain,
empty(empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
( empty(empty_set)
& v5_membered(empty_set)
& v1_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v2_membered(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
fof(f259,plain,
( ~ empty(empty_set)
| empty_carrier(sK1) ),
inference(subsumption_resolution,[],[f252,f146]) ).
fof(f146,plain,
one_sorted_str(sK1),
inference(cnf_transformation,[],[f113]) ).
fof(f252,plain,
( ~ one_sorted_str(sK1)
| empty_carrier(sK1)
| ~ empty(empty_set) ),
inference(superposition,[],[f184,f229]) ).
fof(f229,plain,
empty_set = the_carrier(sK1),
inference(subsumption_resolution,[],[f218,f213]) ).
fof(f213,plain,
~ in(sK3,sK2),
inference(subsumption_resolution,[],[f212,f151]) ).
fof(f151,plain,
element(sK2,powerset(the_carrier(sK1))),
inference(cnf_transformation,[],[f113]) ).
fof(f212,plain,
( ~ element(sK2,powerset(the_carrier(sK1)))
| ~ in(sK3,sK2) ),
inference(duplicate_literal_removal,[],[f208]) ).
fof(f208,plain,
( ~ in(sK3,sK2)
| ~ in(sK3,sK2)
| ~ element(sK2,powerset(the_carrier(sK1))) ),
inference(resolution,[],[f148,f170]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ in(X1,subset_complement(X2,X0))
| ~ element(X0,powerset(X2))
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ element(X0,powerset(X2))
| ~ in(X1,X0)
| ~ in(X1,subset_complement(X2,X0)) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X1))
| ~ in(X0,X2)
| ~ in(X0,subset_complement(X1,X2)) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X2,X1,X0] :
( ~ in(X0,X2)
| ~ in(X0,subset_complement(X1,X2))
| ~ element(X2,powerset(X1)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,plain,
! [X2,X1,X0] :
( element(X2,powerset(X1))
=> ~ ( in(X0,X2)
& in(X0,subset_complement(X1,X2)) ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X1,X0,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f148,plain,
( in(sK3,subset_complement(the_carrier(sK1),sK2))
| ~ in(sK3,sK2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f218,plain,
( empty_set = the_carrier(sK1)
| in(sK3,sK2) ),
inference(subsumption_resolution,[],[f217,f150]) ).
fof(f150,plain,
element(sK3,the_carrier(sK1)),
inference(cnf_transformation,[],[f113]) ).
fof(f217,plain,
( in(sK3,sK2)
| ~ element(sK3,the_carrier(sK1))
| empty_set = the_carrier(sK1) ),
inference(subsumption_resolution,[],[f216,f151]) ).
fof(f216,plain,
( empty_set = the_carrier(sK1)
| ~ element(sK2,powerset(the_carrier(sK1)))
| ~ element(sK3,the_carrier(sK1))
| in(sK3,sK2) ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f215,plain,
( in(sK3,sK2)
| ~ element(sK3,the_carrier(sK1))
| ~ element(sK2,powerset(the_carrier(sK1)))
| empty_set = the_carrier(sK1)
| in(sK3,sK2) ),
inference(resolution,[],[f149,f172]) ).
fof(f172,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| ~ element(X1,powerset(X0))
| ~ element(X2,X0)
| empty_set = X0
| in(X2,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( in(X2,subset_complement(X0,X1))
| ~ element(X2,X0)
| in(X2,X1) ) )
| empty_set = X0 ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( empty_set != X0
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f149,plain,
( ~ in(sK3,subset_complement(the_carrier(sK1),sK2))
| in(sK3,sK2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f184,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 15:10:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.44 % (19955)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.44 % (19946)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.44 % (19955)First to succeed.
% 0.19/0.45 % (19940)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.45 % (19955)Refutation found. Thanks to Tanya!
% 0.19/0.45 % SZS status Theorem for theBenchmark
% 0.19/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.45 % (19955)------------------------------
% 0.19/0.45 % (19955)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.45 % (19955)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.45 % (19955)Termination reason: Refutation
% 0.19/0.45
% 0.19/0.45 % (19955)Memory used [KB]: 1535
% 0.19/0.45 % (19955)Time elapsed: 0.040 s
% 0.19/0.45 % (19955)Instructions burned: 5 (million)
% 0.19/0.45 % (19955)------------------------------
% 0.19/0.45 % (19955)------------------------------
% 0.19/0.45 % (19927)Success in time 0.107 s
%------------------------------------------------------------------------------