TSTP Solution File: SEU321+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n005.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 : Sat Sep 2 00:14:46 EDT 2023
% Result : Theorem 0.17s 0.44s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 9 unt; 0 def)
% Number of atoms : 174 ( 10 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 212 ( 80 ~; 61 |; 52 &)
% ( 2 <=>; 15 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 6 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 : 55 (; 34 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f789,plain,
$false,
inference(resolution,[],[f602,f116]) ).
fof(f116,plain,
empty(empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',fc6_membered) ).
fof(f602,plain,
~ empty(empty_set),
inference(backward_demodulation,[],[f200,f595]) ).
fof(f595,plain,
empty_set = the_carrier(sK3),
inference(resolution,[],[f591,f113]) ).
fof(f113,plain,
element(sK5,the_carrier(sK3)),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( ( in(sK5,sK4)
| ~ in(sK5,subset_complement(the_carrier(sK3),sK4)) )
& ( ~ in(sK5,sK4)
| in(sK5,subset_complement(the_carrier(sK3),sK4)) )
& element(sK5,the_carrier(sK3))
& element(sK4,powerset(the_carrier(sK3)))
& one_sorted_str(sK3)
& ~ empty_carrier(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f89,f92,f91,f90]) ).
fof(f90,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(sK3),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(sK3),X1)) )
& element(X2,the_carrier(sK3)) )
& element(X1,powerset(the_carrier(sK3))) )
& one_sorted_str(sK3)
& ~ empty_carrier(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(sK3),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(sK3),X1)) )
& element(X2,the_carrier(sK3)) )
& element(X1,powerset(the_carrier(sK3))) )
=> ( ? [X2] :
( ( in(X2,sK4)
| ~ in(X2,subset_complement(the_carrier(sK3),sK4)) )
& ( ~ in(X2,sK4)
| in(X2,subset_complement(the_carrier(sK3),sK4)) )
& element(X2,the_carrier(sK3)) )
& element(sK4,powerset(the_carrier(sK3))) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
( ? [X2] :
( ( in(X2,sK4)
| ~ in(X2,subset_complement(the_carrier(sK3),sK4)) )
& ( ~ in(X2,sK4)
| in(X2,subset_complement(the_carrier(sK3),sK4)) )
& element(X2,the_carrier(sK3)) )
=> ( ( in(sK5,sK4)
| ~ in(sK5,subset_complement(the_carrier(sK3),sK4)) )
& ( ~ in(sK5,sK4)
| in(sK5,subset_complement(the_carrier(sK3),sK4)) )
& element(sK5,the_carrier(sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) )
& ( ~ in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(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) ) ) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f40,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(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) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',l40_tops_1) ).
fof(f591,plain,
( ~ element(sK5,the_carrier(sK3))
| empty_set = the_carrier(sK3) ),
inference(resolution,[],[f457,f112]) ).
fof(f112,plain,
element(sK4,powerset(the_carrier(sK3))),
inference(cnf_transformation,[],[f93]) ).
fof(f457,plain,
( ~ element(sK4,powerset(the_carrier(sK3)))
| ~ element(sK5,the_carrier(sK3))
| empty_set = the_carrier(sK3) ),
inference(duplicate_literal_removal,[],[f444]) ).
fof(f444,plain,
( ~ element(sK5,the_carrier(sK3))
| ~ element(sK4,powerset(the_carrier(sK3)))
| empty_set = the_carrier(sK3)
| ~ element(sK4,powerset(the_carrier(sK3))) ),
inference(resolution,[],[f407,f371]) ).
fof(f371,plain,
( ~ in(sK5,sK4)
| ~ element(sK4,powerset(the_carrier(sK3))) ),
inference(duplicate_literal_removal,[],[f368]) ).
fof(f368,plain,
( ~ in(sK5,sK4)
| ~ element(sK4,powerset(the_carrier(sK3)))
| ~ in(sK5,sK4) ),
inference(resolution,[],[f180,f114]) ).
fof(f114,plain,
( in(sK5,subset_complement(the_carrier(sK3),sK4))
| ~ in(sK5,sK4) ),
inference(cnf_transformation,[],[f93]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',t54_subset_1) ).
fof(f407,plain,
( in(sK5,sK4)
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK4,powerset(the_carrier(sK3)))
| empty_set = the_carrier(sK3) ),
inference(duplicate_literal_removal,[],[f401]) ).
fof(f401,plain,
( in(sK5,sK4)
| ~ element(sK5,the_carrier(sK3))
| ~ element(sK4,powerset(the_carrier(sK3)))
| empty_set = the_carrier(sK3)
| in(sK5,sK4) ),
inference(resolution,[],[f165,f115]) ).
fof(f115,plain,
( ~ in(sK5,subset_complement(the_carrier(sK3),sK4))
| in(sK5,sK4) ),
inference(cnf_transformation,[],[f93]) ).
fof(f165,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(flattening,[],[f63]) ).
fof(f63,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/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',t50_subset_1) ).
fof(f200,plain,
~ empty(the_carrier(sK3)),
inference(resolution,[],[f198,f111]) ).
fof(f111,plain,
one_sorted_str(sK3),
inference(cnf_transformation,[],[f93]) ).
fof(f198,plain,
( ~ one_sorted_str(sK3)
| ~ empty(the_carrier(sK3)) ),
inference(resolution,[],[f166,f110]) ).
fof(f110,plain,
~ empty_carrier(sK3),
inference(cnf_transformation,[],[f93]) ).
fof(f166,plain,
! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',fc1_struct_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.34 % Computer : n005.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Wed Aug 30 14:09:37 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.17/0.40 % (15865)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.41 % (15867)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.17/0.41 % (15869)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.41 % (15870)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 Vampire---4 for (531ds/0Mi)
% 0.17/0.41 % (15868)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 Vampire---4 for (569ds/0Mi)
% 0.17/0.41 % (15871)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 Vampire---4 for (522ds/0Mi)
% 0.17/0.41 % (15872)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 Vampire---4 for (497ds/0Mi)
% 0.17/0.41 % (15866)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.17/0.41 TRYING [1]
% 0.17/0.41 TRYING [2]
% 0.17/0.41 TRYING [3]
% 0.17/0.42 TRYING [4]
% 0.17/0.42 TRYING [1]
% 0.17/0.42 TRYING [2]
% 0.17/0.42 TRYING [1]
% 0.17/0.42 TRYING [2]
% 0.17/0.42 TRYING [3]
% 0.17/0.42 TRYING [5]
% 0.17/0.43 TRYING [4]
% 0.17/0.43 TRYING [3]
% 0.17/0.43 TRYING [5]
% 0.17/0.44 TRYING [6]
% 0.17/0.44 % (15871)First to succeed.
% 0.17/0.44 % (15870)Also succeeded, but the first one will report.
% 0.17/0.44 % (15871)Refutation found. Thanks to Tanya!
% 0.17/0.44 % SZS status Theorem for Vampire---4
% 0.17/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.44 % (15871)------------------------------
% 0.17/0.44 % (15871)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.44 % (15871)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.44 % (15871)Termination reason: Refutation
% 0.17/0.44
% 0.17/0.44 % (15871)Memory used [KB]: 1407
% 0.17/0.44 % (15871)Time elapsed: 0.031 s
% 0.17/0.44 % (15871)------------------------------
% 0.17/0.44 % (15871)------------------------------
% 0.17/0.44 % (15865)Success in time 0.094 s
% 0.17/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------