TSTP Solution File: SET931+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n021.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 : Thu Aug 31 15:46:24 EDT 2023
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 14 unt; 0 def)
% Number of atoms : 201 ( 179 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 229 ( 83 ~; 101 |; 38 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 72 (; 60 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f90,plain,
$false,
inference(subsumption_resolution,[],[f50,f89]) ).
fof(f89,plain,
empty_set = sK0,
inference(subsumption_resolution,[],[f88,f86]) ).
fof(f86,plain,
! [X0] :
( empty_set = set_difference(sK0,unordered_pair(sK1,X0))
| empty_set = sK0 ),
inference(superposition,[],[f48,f84]) ).
fof(f84,plain,
( sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(subsumption_resolution,[],[f83,f82]) ).
fof(f82,plain,
! [X1] :
( empty_set = set_difference(sK0,unordered_pair(X1,sK2))
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(superposition,[],[f47,f78]) ).
fof(f78,plain,
( sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f73]) ).
fof(f73,plain,
( sK0 != sK0
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(superposition,[],[f57,f71]) ).
fof(f71,plain,
( sK0 = unordered_pair(sK1,sK2)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f70]) ).
fof(f70,plain,
( empty_set != empty_set
| sK0 = unordered_pair(sK1,sK2)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(duplicate_literal_removal,[],[f69]) ).
fof(f69,plain,
( empty_set != empty_set
| sK0 = unordered_pair(sK1,sK2)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0
| sK0 = singleton(sK1)
| sK0 = singleton(sK2) ),
inference(superposition,[],[f52,f58]) ).
fof(f58,plain,
( empty_set = set_difference(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK1)
| sK0 = singleton(sK2) ),
inference(subsumption_resolution,[],[f51,f57]) ).
fof(f51,plain,
( sK0 = unordered_pair(sK1,sK2)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = set_difference(sK0,unordered_pair(sK1,sK2)) ),
inference(subsumption_resolution,[],[f24,f50]) ).
fof(f24,plain,
( sK0 = unordered_pair(sK1,sK2)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0
| empty_set = set_difference(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ( ( sK0 != unordered_pair(sK1,sK2)
& sK0 != singleton(sK2)
& sK0 != singleton(sK1)
& empty_set != sK0 )
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2)) )
& ( sK0 = unordered_pair(sK1,sK2)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0
| empty_set = set_difference(sK0,unordered_pair(sK1,sK2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
fof(f15,plain,
( ? [X0,X1,X2] :
( ( ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 )
| empty_set != set_difference(X0,unordered_pair(X1,X2)) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| empty_set = set_difference(X0,unordered_pair(X1,X2)) ) )
=> ( ( ( sK0 != unordered_pair(sK1,sK2)
& sK0 != singleton(sK2)
& sK0 != singleton(sK1)
& empty_set != sK0 )
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2)) )
& ( sK0 = unordered_pair(sK1,sK2)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0
| empty_set = set_difference(sK0,unordered_pair(sK1,sK2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ( ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 )
| empty_set != set_difference(X0,unordered_pair(X1,X2)) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| empty_set = set_difference(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1,X2] :
( ( ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 )
| empty_set != set_difference(X0,unordered_pair(X1,X2)) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| empty_set = set_difference(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1,X2] :
( empty_set = set_difference(X0,unordered_pair(X1,X2))
<~> ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( empty_set = set_difference(X0,unordered_pair(X1,X2))
<=> ~ ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X0,X1,X2] :
( empty_set = set_difference(X0,unordered_pair(X1,X2))
<=> ~ ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.UDdQvYiKok/Vampire---4.8_19554',t75_zfmisc_1) ).
fof(f52,plain,
! [X2,X0,X1] :
( empty_set != set_difference(X0,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 ),
inference(forward_literal_rewriting,[],[f34,f32]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.UDdQvYiKok/Vampire---4.8_19554',t37_xboole_1) ).
fof(f34,plain,
! [X2,X0,X1] :
( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.UDdQvYiKok/Vampire---4.8_19554',l46_zfmisc_1) ).
fof(f57,plain,
sK0 != unordered_pair(sK1,sK2),
inference(subsumption_resolution,[],[f45,f55]) ).
fof(f55,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(resolution,[],[f33,f30]) ).
fof(f30,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.UDdQvYiKok/Vampire---4.8_19554',reflexivity_r1_tarski) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f45,plain,
( sK0 != unordered_pair(sK1,sK2)
| empty_set != set_difference(sK0,sK0) ),
inference(inner_rewriting,[],[f28]) ).
fof(f28,plain,
( sK0 != unordered_pair(sK1,sK2)
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f47,plain,
! [X2,X1] : empty_set = set_difference(singleton(X2),unordered_pair(X1,X2)),
inference(forward_literal_rewriting,[],[f42,f33]) ).
fof(f42,plain,
! [X2,X1] : subset(singleton(X2),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f37]) ).
fof(f37,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| singleton(X2) != X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f83,plain,
( empty_set != set_difference(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f80]) ).
fof(f80,plain,
( sK0 != sK0
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(superposition,[],[f27,f78]) ).
fof(f27,plain,
( sK0 != singleton(sK2)
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f48,plain,
! [X2,X1] : empty_set = set_difference(singleton(X1),unordered_pair(X1,X2)),
inference(forward_literal_rewriting,[],[f43,f33]) ).
fof(f43,plain,
! [X2,X1] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f36]) ).
fof(f36,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f88,plain,
( empty_set != set_difference(sK0,unordered_pair(sK1,sK2))
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f85]) ).
fof(f85,plain,
( sK0 != sK0
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2))
| empty_set = sK0 ),
inference(superposition,[],[f26,f84]) ).
fof(f26,plain,
( sK0 != singleton(sK1)
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f50,plain,
empty_set != sK0,
inference(subsumption_resolution,[],[f46,f49]) ).
fof(f49,plain,
! [X2,X1] : empty_set = set_difference(empty_set,unordered_pair(X1,X2)),
inference(forward_literal_rewriting,[],[f44,f33]) ).
fof(f44,plain,
! [X2,X1] : subset(empty_set,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| empty_set != X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
( empty_set != sK0
| empty_set != set_difference(empty_set,unordered_pair(sK1,sK2)) ),
inference(inner_rewriting,[],[f25]) ).
fof(f25,plain,
( empty_set != sK0
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 14:05:11 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.UDdQvYiKok/Vampire---4.8_19554
% 0.15/0.37 % (19663)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (19667)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.22/0.43 % (19666)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.22/0.43 % (19665)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.22/0.43 % (19668)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.22/0.43 % (19669)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.22/0.43 % (19664)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.22/0.43 % (19670)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.22/0.43 % (19668)Refutation not found, incomplete strategy% (19668)------------------------------
% 0.22/0.43 % (19668)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (19668)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (19668)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43
% 0.22/0.43 % (19668)Memory used [KB]: 895
% 0.22/0.43 % (19668)Time elapsed: 0.003 s
% 0.22/0.43 % (19668)------------------------------
% 0.22/0.43 % (19668)------------------------------
% 0.22/0.43 % (19669)First to succeed.
% 0.22/0.43 % (19667)Also succeeded, but the first one will report.
% 0.22/0.43 % (19665)Also succeeded, but the first one will report.
% 0.22/0.43 % (19669)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for Vampire---4
% 0.22/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.44 % (19669)------------------------------
% 0.22/0.44 % (19669)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.44 % (19669)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.44 % (19669)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (19669)Memory used [KB]: 1023
% 0.22/0.44 % (19669)Time elapsed: 0.006 s
% 0.22/0.44 % (19669)------------------------------
% 0.22/0.44 % (19669)------------------------------
% 0.22/0.44 % (19663)Success in time 0.064 s
% 0.22/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------