TSTP Solution File: SET637+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n022.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 15:44:57 EDT 2023
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 9 unt; 0 def)
% Number of atoms : 200 ( 28 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 229 ( 94 ~; 93 |; 30 &)
% ( 7 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 104 (; 91 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f185,plain,
$false,
inference(resolution,[],[f182,f175]) ).
fof(f175,plain,
intersect(sK0,sK1),
inference(resolution,[],[f168,f46]) ).
fof(f46,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox/tmp/tmp.Z3s0ovFuz6/Vampire---4.8_20155',not_equal_defn) ).
fof(f168,plain,
( not_equal(empty_set,empty_set)
| intersect(sK0,sK1) ),
inference(backward_demodulation,[],[f49,f164]) ).
fof(f164,plain,
empty_set = sF4,
inference(duplicate_literal_removal,[],[f153]) ).
fof(f153,plain,
( empty_set = sF4
| empty_set = sF4 ),
inference(resolution,[],[f139,f29]) ).
fof(f29,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/tmp/tmp.Z3s0ovFuz6/Vampire---4.8_20155',empty_set_defn) ).
fof(f139,plain,
! [X10] :
( member(sK2(X10,sF4),X10)
| sF4 = X10
| empty_set = sF4 ),
inference(resolution,[],[f34,f124]) ).
fof(f124,plain,
! [X0] :
( ~ member(X0,sF4)
| empty_set = sF4 ),
inference(factoring,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ~ member(X0,sF4)
| ~ member(X0,X1)
| empty_set = sF4 ),
inference(resolution,[],[f112,f40]) ).
fof(f40,plain,
! [X2,X0,X1] :
( intersect(X0,X1)
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ( member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) )
| ~ intersect(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
=> ( member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.Z3s0ovFuz6/Vampire---4.8_20155',intersect_defn) ).
fof(f112,plain,
! [X0] :
( ~ intersect(sF4,X0)
| empty_set = sF4 ),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ~ intersect(sF4,X0)
| empty_set = sF4
| ~ intersect(sF4,X0) ),
inference(resolution,[],[f85,f38]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f85,plain,
! [X0] :
( ~ member(sK3(sF4,X0),sF4)
| ~ intersect(sF4,X0)
| empty_set = sF4 ),
inference(resolution,[],[f75,f61]) ).
fof(f61,plain,
! [X0] :
( member(X0,sK0)
| ~ member(X0,sF4) ),
inference(superposition,[],[f41,f47]) ).
fof(f47,plain,
intersection(sK0,sK1) = sF4,
introduced(function_definition,[]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.Z3s0ovFuz6/Vampire---4.8_20155',intersection_defn) ).
fof(f75,plain,
! [X0] :
( ~ member(sK3(sF4,X0),sK0)
| empty_set = sF4
| ~ intersect(sF4,X0) ),
inference(resolution,[],[f74,f38]) ).
fof(f74,plain,
! [X2] :
( ~ member(X2,sF4)
| empty_set = sF4
| ~ member(X2,sK0) ),
inference(resolution,[],[f69,f66]) ).
fof(f66,plain,
! [X0] :
( member(X0,sK1)
| ~ member(X0,sF4) ),
inference(superposition,[],[f42,f47]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f69,plain,
! [X0] :
( ~ member(X0,sK1)
| ~ member(X0,sK0)
| empty_set = sF4 ),
inference(resolution,[],[f40,f51]) ).
fof(f51,plain,
( ~ intersect(sK0,sK1)
| empty_set = sF4 ),
inference(resolution,[],[f37,f48]) ).
fof(f48,plain,
( ~ not_equal(sF4,empty_set)
| ~ intersect(sK0,sK1) ),
inference(definition_folding,[],[f28,f47]) ).
fof(f28,plain,
( ~ not_equal(intersection(sK0,sK1),empty_set)
| ~ intersect(sK0,sK1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( ( ~ not_equal(intersection(sK0,sK1),empty_set)
| ~ intersect(sK0,sK1) )
& ( not_equal(intersection(sK0,sK1),empty_set)
| intersect(sK0,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
fof(f14,plain,
( ? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) )
=> ( ( ~ not_equal(intersection(sK0,sK1),empty_set)
| ~ intersect(sK0,sK1) )
& ( not_equal(intersection(sK0,sK1),empty_set)
| intersect(sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1] :
( intersect(X0,X1)
<~> not_equal(intersection(X0,X1),empty_set) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
file('/export/starexec/sandbox/tmp/tmp.Z3s0ovFuz6/Vampire---4.8_20155',prove_th119) ).
fof(f37,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| X0 = X1
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f18]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.Z3s0ovFuz6/Vampire---4.8_20155',equal_member_defn) ).
fof(f49,plain,
( not_equal(sF4,empty_set)
| intersect(sK0,sK1) ),
inference(definition_folding,[],[f27,f47]) ).
fof(f27,plain,
( not_equal(intersection(sK0,sK1),empty_set)
| intersect(sK0,sK1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f182,plain,
~ intersect(sK0,sK1),
inference(forward_literal_rewriting,[],[f181,f31]) ).
fof(f31,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.Z3s0ovFuz6/Vampire---4.8_20155',symmetry_of_intersect) ).
fof(f181,plain,
~ intersect(sK1,sK0),
inference(duplicate_literal_removal,[],[f180]) ).
fof(f180,plain,
( ~ intersect(sK1,sK0)
| ~ intersect(sK1,sK0) ),
inference(resolution,[],[f177,f39]) ).
fof(f39,plain,
! [X0,X1] :
( member(sK3(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f177,plain,
! [X0] :
( ~ member(sK3(sK1,X0),sK0)
| ~ intersect(sK1,X0) ),
inference(resolution,[],[f176,f38]) ).
fof(f176,plain,
! [X0] :
( ~ member(X0,sK1)
| ~ member(X0,sK0) ),
inference(resolution,[],[f171,f29]) ).
fof(f171,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK1)
| ~ member(X0,sK0) ),
inference(backward_demodulation,[],[f96,f164]) ).
fof(f96,plain,
! [X0] :
( member(X0,sF4)
| ~ member(X0,sK1)
| ~ member(X0,sK0) ),
inference(superposition,[],[f43,f47]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 14:24:55 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.Z3s0ovFuz6/Vampire---4.8_20155
% 0.14/0.36 % (20467)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (20471)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)
% 0.21/0.42 % (20473)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)
% 0.21/0.42 % (20477)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)
% 0.21/0.42 % (20472)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)
% 0.21/0.42 % (20474)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)
% 0.21/0.42 % (20470)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)
% 0.21/0.42 % (20475)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)
% 0.21/0.43 % (20472)First to succeed.
% 0.21/0.43 % (20472)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for Vampire---4
% 0.21/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.43 % (20472)------------------------------
% 0.21/0.43 % (20472)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.43 % (20472)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.43 % (20472)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (20472)Memory used [KB]: 1023
% 0.21/0.43 % (20472)Time elapsed: 0.008 s
% 0.21/0.43 % (20472)------------------------------
% 0.21/0.43 % (20472)------------------------------
% 0.21/0.43 % (20467)Success in time 0.067 s
% 0.21/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------