TSTP Solution File: SET931+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---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 : n028.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 00:05:50 EDT 2023
% Result : Theorem 0.16s 0.39s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 14 unt; 0 def)
% Number of atoms : 167 ( 140 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 198 ( 76 ~; 77 |; 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 : 62 (; 50 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f144,plain,
$false,
inference(unit_resulting_resolution,[],[f89,f127,f128,f86,f124,f34]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ subset(X0,unordered_pair(X1,X2))
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| unordered_pair(X1,X2) = X0 ),
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/sandbox2/tmp/tmp.ipHghAsRh0/Vampire---4.8_12516',l46_zfmisc_1) ).
fof(f124,plain,
subset(sK0,unordered_pair(sK1,sK2)),
inference(subsumption_resolution,[],[f123,f36]) ).
fof(f36,plain,
! [X2,X0,X1] :
( singleton(X1) != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f123,plain,
( subset(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK1) ),
inference(subsumption_resolution,[],[f122,f37]) ).
fof(f37,plain,
! [X2,X0,X1] :
( singleton(X2) != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f122,plain,
( subset(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK2)
| sK0 = singleton(sK1) ),
inference(subsumption_resolution,[],[f121,f86]) ).
fof(f121,plain,
( subset(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| sK0 = unordered_pair(sK1,sK2) ),
inference(subsumption_resolution,[],[f120,f89]) ).
fof(f120,plain,
( subset(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0
| sK0 = unordered_pair(sK1,sK2) ),
inference(trivial_inequality_removal,[],[f119]) ).
fof(f119,plain,
( empty_set != empty_set
| subset(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0
| sK0 = unordered_pair(sK1,sK2) ),
inference(superposition,[],[f32,f24]) ).
fof(f24,plain,
( empty_set = set_difference(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0
| 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/sandbox2/tmp/tmp.ipHghAsRh0/Vampire---4.8_12516',t75_zfmisc_1) ).
fof(f32,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(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/sandbox2/tmp/tmp.ipHghAsRh0/Vampire---4.8_12516',t37_xboole_1) ).
fof(f86,plain,
sK0 != unordered_pair(sK1,sK2),
inference(unit_resulting_resolution,[],[f43,f41]) ).
fof(f41,plain,
( empty_set != set_difference(sK0,sK0)
| sK0 != unordered_pair(sK1,sK2) ),
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(f43,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(unit_resulting_resolution,[],[f30,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
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/sandbox2/tmp/tmp.ipHghAsRh0/Vampire---4.8_12516',reflexivity_r1_tarski) ).
fof(f128,plain,
sK0 != singleton(sK1),
inference(unit_resulting_resolution,[],[f125,f26]) ).
fof(f26,plain,
( empty_set != set_difference(sK0,unordered_pair(sK1,sK2))
| sK0 != singleton(sK1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f125,plain,
empty_set = set_difference(sK0,unordered_pair(sK1,sK2)),
inference(unit_resulting_resolution,[],[f124,f33]) ).
fof(f127,plain,
sK0 != singleton(sK2),
inference(unit_resulting_resolution,[],[f125,f27]) ).
fof(f27,plain,
( empty_set != set_difference(sK0,unordered_pair(sK1,sK2))
| sK0 != singleton(sK2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f89,plain,
empty_set != sK0,
inference(unit_resulting_resolution,[],[f51,f42]) ).
fof(f42,plain,
( empty_set != set_difference(empty_set,unordered_pair(sK1,sK2))
| empty_set != sK0 ),
inference(inner_rewriting,[],[f25]) ).
fof(f25,plain,
( empty_set != sK0
| empty_set != set_difference(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f51,plain,
! [X0,X1] : empty_set = set_difference(empty_set,unordered_pair(X0,X1)),
inference(unit_resulting_resolution,[],[f50,f33]) ).
fof(f50,plain,
! [X2,X1] : subset(empty_set,unordered_pair(X1,X2)),
inference(forward_demodulation,[],[f48,f43]) ).
fof(f48,plain,
! [X2,X0,X1] : subset(set_difference(X0,X0),unordered_pair(X1,X2)),
inference(unit_resulting_resolution,[],[f43,f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( empty_set != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 30 16:03:27 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % (12622)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.39 % (12625)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)
% 0.11/0.39 % (12624)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.11/0.39 % (12627)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)
% 0.11/0.39 % (12628)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)
% 0.11/0.39 % (12629)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)
% 0.11/0.39 % (12626)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.16/0.39 % (12623)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 % (12629)First to succeed.
% 0.16/0.39 TRYING [4]
% 0.16/0.39 % (12627)Also succeeded, but the first one will report.
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 TRYING [5]
% 0.16/0.39 % (12628)Also succeeded, but the first one will report.
% 0.16/0.39 TRYING [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 % (12629)Refutation found. Thanks to Tanya!
% 0.16/0.39 % SZS status Theorem for Vampire---4
% 0.16/0.39 % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.39 % (12629)------------------------------
% 0.16/0.39 % (12629)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.39 % (12629)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.39 % (12629)Termination reason: Refutation
% 0.16/0.39
% 0.16/0.39 % (12629)Memory used [KB]: 895
% 0.16/0.39 % (12629)Time elapsed: 0.006 s
% 0.16/0.39 % (12629)------------------------------
% 0.16/0.39 % (12629)------------------------------
% 0.16/0.39 % (12622)Success in time 0.051 s
% 0.16/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------