0.11/0.26	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.26	% Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
0.12/0.46	% Computer : n027.cluster.edu
0.12/0.46	% Model    : x86_64 x86_64
0.12/0.46	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.46	% Memory   : 8042.1875MB
0.12/0.46	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.47	% CPULimit   : 300
0.12/0.47	% WCLimit    : 300
0.12/0.47	% DateTime   : Fri Jul  5 04:21:40 EDT 2024
0.12/0.47	% CPUTime    : 
0.19/0.49	This is a TFF_ problem
0.19/0.49	Running vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
0.19/0.49	% (7188)Running in auto input_syntax mode. Trying TPTP
0.19/0.54	% (7193)lrs+1010_2:1_amm=off:bs=on:bsr=on:canc=force:fsd=off:fsr=off:gs=on:gsaa=full_model:gsem=on:nm=0:nwc=1.3:sas=z3:sac=on:tha=off:thi=overlap:tgt=ground:uwa=ground:stl=60_408 on theBenchmark for (408ds/0Mi)
0.19/0.55	% (7194)ott+10_1024_av=off:bd=preordered:br=off:ep=RSTC:fsr=off:fde=none:nm=2:urr=on_318 on theBenchmark for (318ds/0Mi)
0.19/0.55	% (7195)lrs-1010_3_av=off:br=off:drc=off:er=known:fsd=off:fde=unused:nm=4:nwc=3.0:sp=scramble:urr=on:stl=180_280 on theBenchmark for (280ds/0Mi)
0.19/0.55	% (7190)dis-1010_2:3_canc=force:fsd=off:fde=unused:gs=on:gsem=on:nm=0:nwc=1.3:sas=z3:tha=off:thf=on:uwa=ground_572 on theBenchmark for (572ds/0Mi)
0.19/0.55	% (7189)lrs+2_32_add=large:amm=off:bd=off:bs=unit_only:drc=off:flr=on:fsd=off:fde=none:nm=0:nwc=1.1:sos=theory:sp=reverse_arity:tgt=ground:stl=180_1034 on theBenchmark for (1034ds/0Mi)
0.19/0.55	% (7192)dis-11_10:1_canc=force:fsd=off:nwc=1.5:sas=z3:tha=off:uwa=all_472 on theBenchmark for (472ds/0Mi)
0.19/0.55	% (7191)dis-10_20_canc=force:fsd=off:gs=on:gsem=off:nm=0:sas=z3:sac=on:tha=off:thi=strong:tgt=ground_476 on theBenchmark for (476ds/0Mi)
1.13/0.66	% (7192)First to succeed.
1.13/0.66	% (7192)Refutation found. Thanks to Tanya!
1.13/0.66	% SZS status Theorem for theBenchmark
1.13/0.66	% SZS output start Proof for theBenchmark
1.13/0.66	tff(type_def_5, type, set: $tType).
1.13/0.66	tff(type_def_6, type, element: $tType).
1.13/0.66	tff(func_def_0, type, empty_set: set).
1.13/0.66	tff(func_def_1, type, singleton: element > set).
1.13/0.66	tff(func_def_2, type, intersection: (set * set) > set).
1.13/0.66	tff(func_def_3, type, union: (set * set) > set).
1.13/0.66	tff(func_def_4, type, difference: (set * set) > set).
1.13/0.66	tff(func_def_5, type, complement: set > set).
1.13/0.66	tff(func_def_6, type, cardinality: set > $int).
1.13/0.66	tff(func_def_10, type, sK0: element).
1.13/0.66	tff(func_def_11, type, sK1: set).
1.13/0.66	tff(func_def_12, type, sK2: $int).
1.13/0.66	tff(func_def_13, type, sK3: set > element).
1.13/0.66	tff(pred_def_1, type, member: (element * set) > $o).
1.13/0.66	tff(pred_def_2, type, subset: (set * set) > $o).
1.13/0.66	tff(f2479,plain,(
1.13/0.66	  $false),
1.13/0.66	  inference(avatar_smt_refutation,[],[f82,f87,f92,f97,f110,f256,f270,f969,f998,f1587,f1617,f1816,f1827,f1829,f2467,f2473,f2476,f2478])).
1.13/0.66	tff(f2478,plain,(
1.13/0.66	  ~spl4_16 | ~spl4_17 | spl4_9 | ~spl4_14),
1.13/0.66	  inference(avatar_split_clause,[],[f2477,f1614,f963,f1824,f1820])).
1.13/0.66	tff(f1820,plain,(
1.13/0.66	  spl4_16 <=> member(sK3(complement(empty_set)),singleton(sK0))),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_16])])).
1.13/0.66	tff(f1824,plain,(
1.13/0.66	  spl4_17 <=> member(sK3(complement(empty_set)),sK1)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_17])])).
1.13/0.66	tff(f963,plain,(
1.13/0.66	  spl4_9 <=> empty_set = complement(empty_set)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_9])])).
1.13/0.66	tff(f1614,plain,(
1.13/0.66	  spl4_14 <=> empty_set = intersection(singleton(sK0),sK1)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_14])])).
1.13/0.66	tff(f2477,plain,(
1.13/0.66	  ~member(sK3(complement(empty_set)),sK1) | ~member(sK3(complement(empty_set)),singleton(sK0)) | (spl4_9 | ~spl4_14)),
1.13/0.66	  inference(subsumption_resolution,[],[f2433,f965])).
1.13/0.66	tff(f965,plain,(
1.13/0.66	  empty_set != complement(empty_set) | spl4_9),
1.13/0.66	  inference(avatar_component_clause,[],[f963])).
1.13/0.66	tff(f2433,plain,(
1.13/0.66	  ~member(sK3(complement(empty_set)),sK1) | ~member(sK3(complement(empty_set)),singleton(sK0)) | empty_set = complement(empty_set) | ~spl4_14),
1.13/0.66	  inference(superposition,[],[f132,f1616])).
1.13/0.66	tff(f1616,plain,(
1.13/0.66	  empty_set = intersection(singleton(sK0),sK1) | ~spl4_14),
1.13/0.66	  inference(avatar_component_clause,[],[f1614])).
1.13/0.66	tff(f132,plain,(
1.13/0.66	  ( ! [X0 : set,X1 : set] : (~member(sK3(complement(intersection(X0,X1))),X0) | ~member(sK3(complement(intersection(X0,X1))),X1) | empty_set = complement(intersection(X0,X1))) )),
1.13/0.66	  inference(resolution,[],[f113,f68])).
1.13/0.66	tff(f68,plain,(
1.13/0.66	  ( ! [X2 : set,X0 : element,X1 : set] : (member(X0,intersection(X1,X2)) | ~member(X0,X1) | ~member(X0,X2)) )),
1.13/0.66	  inference(cnf_transformation,[],[f42])).
1.13/0.66	tff(f42,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : ((member(X0,intersection(X1,X2)) | ~member(X0,X1) | ~member(X0,X2)) & ((member(X0,X1) & member(X0,X2)) | ~member(X0,intersection(X1,X2))))),
1.13/0.66	  inference(flattening,[],[f41])).
1.13/0.66	tff(f41,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : ((member(X0,intersection(X1,X2)) | (~member(X0,X1) | ~member(X0,X2))) & ((member(X0,X1) & member(X0,X2)) | ~member(X0,intersection(X1,X2))))),
1.13/0.66	  inference(nnf_transformation,[],[f23])).
1.13/0.66	tff(f23,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : (member(X0,intersection(X1,X2)) <=> (member(X0,X1) & member(X0,X2)))),
1.13/0.66	  inference(rectify,[],[f12])).
1.13/0.66	tff(f12,axiom,(
1.13/0.66	  ! [X2 : element,X0 : set,X1 : set] : (member(X2,intersection(X0,X1)) <=> (member(X2,X0) & member(X2,X1)))),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection)).
1.13/0.66	tff(f113,plain,(
1.13/0.66	  ( ! [X2 : set] : (~member(sK3(complement(X2)),X2) | empty_set = complement(X2)) )),
1.13/0.66	  inference(resolution,[],[f55,f53])).
1.13/0.66	tff(f53,plain,(
1.13/0.66	  ( ! [X0 : set] : (member(sK3(X0),X0) | empty_set = X0) )),
1.13/0.66	  inference(cnf_transformation,[],[f34])).
1.13/0.66	tff(f34,plain,(
1.13/0.66	  ! [X0 : set] : ((empty_set = X0 | member(sK3(X0),X0)) & (! [X2 : element] : ~member(X2,X0) | empty_set != X0))),
1.13/0.66	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f32,f33])).
1.13/0.66	tff(f33,plain,(
1.13/0.66	  ! [X0 : set] : (? [X1 : element] : member(X1,X0) => member(sK3(X0),X0))),
1.13/0.66	  introduced(choice_axiom,[])).
1.13/0.66	tff(f32,plain,(
1.13/0.66	  ! [X0 : set] : ((empty_set = X0 | ? [X1 : element] : member(X1,X0)) & (! [X2 : element] : ~member(X2,X0) | empty_set != X0))),
1.13/0.66	  inference(rectify,[],[f31])).
1.13/0.66	tff(f31,plain,(
1.13/0.66	  ! [X0 : set] : ((empty_set = X0 | ? [X1 : element] : member(X1,X0)) & (! [X1 : element] : ~member(X1,X0) | empty_set != X0))),
1.13/0.66	  inference(nnf_transformation,[],[f17])).
1.13/0.66	tff(f17,plain,(
1.13/0.66	  ! [X0 : set] : (empty_set = X0 <=> ! [X1 : element] : ~member(X1,X0))),
1.13/0.66	  inference(rectify,[],[f10])).
1.13/0.66	tff(f10,axiom,(
1.13/0.66	  ! [X5 : set] : (empty_set = X5 <=> ! [X2 : element] : ~member(X2,X5))),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set)).
1.13/0.66	tff(f55,plain,(
1.13/0.66	  ( ! [X0 : element,X1 : set] : (~member(X0,complement(X1)) | ~member(X0,X1)) )),
1.13/0.66	  inference(cnf_transformation,[],[f35])).
1.13/0.66	tff(f35,plain,(
1.13/0.66	  ! [X0 : element,X1 : set] : ((~member(X0,complement(X1)) | ~member(X0,X1)) & (member(X0,X1) | member(X0,complement(X1))))),
1.13/0.66	  inference(nnf_transformation,[],[f18])).
1.13/0.66	tff(f18,plain,(
1.13/0.66	  ! [X0 : element,X1 : set] : (~member(X0,complement(X1)) <=> member(X0,X1))),
1.13/0.66	  inference(rectify,[],[f5])).
1.13/0.66	tff(f5,axiom,(
1.13/0.66	  ! [X2 : element,X5 : set] : (~member(X2,complement(X5)) <=> member(X2,X5))),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement)).
1.13/0.66	tff(f2476,plain,(
1.13/0.66	  ~spl4_17 | ~spl4_16 | spl4_9 | ~spl4_14),
1.13/0.66	  inference(avatar_split_clause,[],[f2475,f1614,f963,f1820,f1824])).
1.13/0.66	tff(f2475,plain,(
1.13/0.66	  ~member(sK3(complement(empty_set)),singleton(sK0)) | ~member(sK3(complement(empty_set)),sK1) | (spl4_9 | ~spl4_14)),
1.13/0.66	  inference(subsumption_resolution,[],[f2432,f965])).
1.13/0.66	tff(f2432,plain,(
1.13/0.66	  ~member(sK3(complement(empty_set)),singleton(sK0)) | ~member(sK3(complement(empty_set)),sK1) | empty_set = complement(empty_set) | ~spl4_14),
1.13/0.66	  inference(superposition,[],[f132,f1616])).
1.13/0.66	tff(f2473,plain,(
1.13/0.66	  spl4_18 | ~spl4_3 | ~spl4_14),
1.13/0.66	  inference(avatar_split_clause,[],[f2468,f1614,f89,f2470])).
1.13/0.66	tff(f2470,plain,(
1.13/0.66	  spl4_18 <=> cardinality(union(singleton(sK0),sK1)) = $sum(cardinality(singleton(sK0)),sK2)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_18])])).
1.13/0.66	tff(f89,plain,(
1.13/0.66	  spl4_3 <=> sK2 = cardinality(sK1)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_3])])).
1.13/0.66	tff(f2468,plain,(
1.13/0.66	  cardinality(union(singleton(sK0),sK1)) = $sum(cardinality(singleton(sK0)),sK2) | (~spl4_3 | ~spl4_14)),
1.13/0.66	  inference(forward_demodulation,[],[f2462,f91])).
1.13/0.66	tff(f91,plain,(
1.13/0.66	  sK2 = cardinality(sK1) | ~spl4_3),
1.13/0.66	  inference(avatar_component_clause,[],[f89])).
1.13/0.66	tff(f2462,plain,(
1.13/0.66	  cardinality(union(singleton(sK0),sK1)) = $sum(cardinality(singleton(sK0)),cardinality(sK1)) | ~spl4_14),
1.13/0.66	  inference(trivial_inequality_removal,[],[f2426])).
1.13/0.66	tff(f2426,plain,(
1.13/0.66	  empty_set != empty_set | cardinality(union(singleton(sK0),sK1)) = $sum(cardinality(singleton(sK0)),cardinality(sK1)) | ~spl4_14),
1.13/0.66	  inference(superposition,[],[f63,f1616])).
1.13/0.66	tff(f63,plain,(
1.13/0.66	  ( ! [X0 : set,X1 : set] : (intersection(X0,X1) != empty_set | cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1))) )),
1.13/0.66	  inference(cnf_transformation,[],[f39])).
1.13/0.66	tff(f39,plain,(
1.13/0.66	  ! [X0 : set,X1 : set] : ((cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1)) | intersection(X0,X1) != empty_set) & (intersection(X0,X1) = empty_set | cardinality(union(X0,X1)) != $sum(cardinality(X0),cardinality(X1))))),
1.13/0.66	  inference(nnf_transformation,[],[f1])).
1.13/0.66	tff(f1,axiom,(
1.13/0.66	  ! [X0 : set,X1 : set] : (cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1)) <=> intersection(X0,X1) = empty_set)),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cardinality_union)).
1.13/0.66	tff(f2467,plain,(
1.13/0.66	  spl4_1 | ~spl4_3 | ~spl4_14),
1.13/0.66	  inference(avatar_contradiction_clause,[],[f2466])).
1.13/0.66	tff(f2466,plain,(
1.13/0.66	  $false | (spl4_1 | ~spl4_3 | ~spl4_14)),
1.13/0.66	  inference(subsumption_resolution,[],[f2465,f81])).
1.13/0.66	tff(f81,plain,(
1.13/0.66	  $sum(sK2,1) != cardinality(union(singleton(sK0),sK1)) | spl4_1),
1.13/0.66	  inference(avatar_component_clause,[],[f79])).
1.13/0.66	tff(f79,plain,(
1.13/0.66	  spl4_1 <=> $sum(sK2,1) = cardinality(union(singleton(sK0),sK1))),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_1])])).
1.13/0.66	tff(f2465,plain,(
1.13/0.66	  $sum(sK2,1) = cardinality(union(singleton(sK0),sK1)) | (~spl4_3 | ~spl4_14)),
1.13/0.66	  inference(forward_demodulation,[],[f2464,f91])).
1.13/0.66	tff(f2464,plain,(
1.13/0.66	  cardinality(union(singleton(sK0),sK1)) = $sum(cardinality(sK1),1) | ~spl4_14),
1.13/0.66	  inference(trivial_inequality_removal,[],[f2423])).
1.13/0.66	tff(f2423,plain,(
1.13/0.66	  empty_set != empty_set | cardinality(union(singleton(sK0),sK1)) = $sum(cardinality(sK1),1) | ~spl4_14),
1.13/0.66	  inference(superposition,[],[f65,f1616])).
1.13/0.66	tff(f65,plain,(
1.13/0.66	  ( ! [X0 : element,X1 : set] : (empty_set != intersection(singleton(X0),X1) | cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1)) )),
1.13/0.66	  inference(cnf_transformation,[],[f40])).
1.13/0.66	tff(f40,plain,(
1.13/0.66	  ! [X0 : element,X1 : set] : ((cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) | empty_set != intersection(singleton(X0),X1)) & (empty_set = intersection(singleton(X0),X1) | cardinality(union(singleton(X0),X1)) != $sum(cardinality(X1),1)))),
1.13/0.66	  inference(nnf_transformation,[],[f22])).
1.13/0.66	tff(f22,plain,(
1.13/0.66	  ! [X0 : element,X1 : set] : (cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) <=> empty_set = intersection(singleton(X0),X1))),
1.13/0.66	  inference(rectify,[],[f9])).
1.13/0.66	tff(f9,axiom,(
1.13/0.66	  ! [X2 : element,X5 : set] : (cardinality(union(singleton(X2),X5)) = $sum(cardinality(X5),1) <=> empty_set = intersection(singleton(X2),X5))),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cardinality_intersection_2)).
1.13/0.66	tff(f1829,plain,(
1.13/0.66	  ~spl4_17 | ~spl4_16 | spl4_9 | ~spl4_13),
1.13/0.66	  inference(avatar_split_clause,[],[f1828,f1584,f963,f1820,f1824])).
1.13/0.66	tff(f1584,plain,(
1.13/0.66	  spl4_13 <=> empty_set = intersection(sK1,singleton(sK0))),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_13])])).
1.13/0.66	tff(f1828,plain,(
1.13/0.66	  ~member(sK3(complement(empty_set)),singleton(sK0)) | ~member(sK3(complement(empty_set)),sK1) | (spl4_9 | ~spl4_13)),
1.13/0.66	  inference(subsumption_resolution,[],[f1786,f965])).
1.13/0.66	tff(f1786,plain,(
1.13/0.66	  ~member(sK3(complement(empty_set)),singleton(sK0)) | ~member(sK3(complement(empty_set)),sK1) | empty_set = complement(empty_set) | ~spl4_13),
1.13/0.66	  inference(superposition,[],[f132,f1586])).
1.13/0.66	tff(f1586,plain,(
1.13/0.66	  empty_set = intersection(sK1,singleton(sK0)) | ~spl4_13),
1.13/0.66	  inference(avatar_component_clause,[],[f1584])).
1.13/0.66	tff(f1827,plain,(
1.13/0.66	  ~spl4_16 | ~spl4_17 | spl4_9 | ~spl4_13),
1.13/0.66	  inference(avatar_split_clause,[],[f1818,f1584,f963,f1824,f1820])).
1.13/0.66	tff(f1818,plain,(
1.13/0.66	  ~member(sK3(complement(empty_set)),sK1) | ~member(sK3(complement(empty_set)),singleton(sK0)) | (spl4_9 | ~spl4_13)),
1.13/0.66	  inference(subsumption_resolution,[],[f1785,f965])).
1.13/0.66	tff(f1785,plain,(
1.13/0.66	  ~member(sK3(complement(empty_set)),sK1) | ~member(sK3(complement(empty_set)),singleton(sK0)) | empty_set = complement(empty_set) | ~spl4_13),
1.13/0.66	  inference(superposition,[],[f132,f1586])).
1.13/0.66	tff(f1816,plain,(
1.13/0.66	  spl4_15 | ~spl4_3 | ~spl4_13),
1.13/0.66	  inference(avatar_split_clause,[],[f1811,f1584,f89,f1813])).
1.13/0.66	tff(f1813,plain,(
1.13/0.66	  spl4_15 <=> cardinality(union(sK1,singleton(sK0))) = $sum(sK2,cardinality(singleton(sK0)))),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_15])])).
1.13/0.66	tff(f1811,plain,(
1.13/0.66	  cardinality(union(sK1,singleton(sK0))) = $sum(sK2,cardinality(singleton(sK0))) | (~spl4_3 | ~spl4_13)),
1.13/0.66	  inference(forward_demodulation,[],[f1809,f91])).
1.13/0.66	tff(f1809,plain,(
1.13/0.66	  cardinality(union(sK1,singleton(sK0))) = $sum(cardinality(sK1),cardinality(singleton(sK0))) | ~spl4_13),
1.13/0.66	  inference(trivial_inequality_removal,[],[f1779])).
1.13/0.66	tff(f1779,plain,(
1.13/0.66	  empty_set != empty_set | cardinality(union(sK1,singleton(sK0))) = $sum(cardinality(sK1),cardinality(singleton(sK0))) | ~spl4_13),
1.13/0.66	  inference(superposition,[],[f63,f1586])).
1.13/0.66	tff(f1617,plain,(
1.13/0.66	  spl4_14 | spl4_2),
1.13/0.66	  inference(avatar_split_clause,[],[f1588,f84,f1614])).
1.13/0.66	tff(f84,plain,(
1.13/0.66	  spl4_2 <=> member(sK0,sK1)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_2])])).
1.13/0.66	tff(f1588,plain,(
1.13/0.66	  empty_set = intersection(singleton(sK0),sK1) | spl4_2),
1.13/0.66	  inference(resolution,[],[f311,f86])).
1.13/0.66	tff(f86,plain,(
1.13/0.66	  ~member(sK0,sK1) | spl4_2),
1.13/0.66	  inference(avatar_component_clause,[],[f84])).
1.13/0.66	tff(f311,plain,(
1.13/0.66	  ( ! [X2 : element,X3 : set] : (member(X2,X3) | empty_set = intersection(singleton(X2),X3)) )),
1.13/0.66	  inference(duplicate_literal_removal,[],[f304])).
1.13/0.66	tff(f304,plain,(
1.13/0.66	  ( ! [X2 : element,X3 : set] : (member(X2,X3) | empty_set = intersection(singleton(X2),X3) | empty_set = intersection(singleton(X2),X3)) )),
1.13/0.66	  inference(superposition,[],[f116,f184])).
1.13/0.66	tff(f184,plain,(
1.13/0.66	  ( ! [X4 : element,X5 : set] : (sK3(intersection(singleton(X4),X5)) = X4 | empty_set = intersection(singleton(X4),X5)) )),
1.13/0.66	  inference(resolution,[],[f121,f56])).
1.13/0.66	tff(f56,plain,(
1.13/0.66	  ( ! [X0 : element,X1 : element] : (~member(X0,singleton(X1)) | X0 = X1) )),
1.13/0.66	  inference(cnf_transformation,[],[f36])).
1.13/0.66	tff(f36,plain,(
1.13/0.66	  ! [X0 : element,X1 : element] : ((member(X0,singleton(X1)) | X0 != X1) & (X0 = X1 | ~member(X0,singleton(X1))))),
1.13/0.66	  inference(nnf_transformation,[],[f19])).
1.13/0.66	tff(f19,plain,(
1.13/0.66	  ! [X0 : element,X1 : element] : (member(X0,singleton(X1)) <=> X0 = X1)),
1.13/0.66	  inference(rectify,[],[f7])).
1.13/0.66	tff(f7,axiom,(
1.13/0.66	  ! [X2 : element,X0 : element] : (member(X2,singleton(X0)) <=> X0 = X2)),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
1.13/0.66	tff(f121,plain,(
1.13/0.66	  ( ! [X0 : set,X1 : set] : (member(sK3(intersection(X0,X1)),X0) | intersection(X0,X1) = empty_set) )),
1.13/0.66	  inference(resolution,[],[f67,f53])).
1.13/0.66	tff(f67,plain,(
1.13/0.66	  ( ! [X2 : set,X0 : element,X1 : set] : (~member(X0,intersection(X1,X2)) | member(X0,X1)) )),
1.13/0.66	  inference(cnf_transformation,[],[f42])).
1.13/0.66	tff(f116,plain,(
1.13/0.66	  ( ! [X0 : set,X1 : set] : (member(sK3(intersection(X0,X1)),X1) | intersection(X0,X1) = empty_set) )),
1.13/0.66	  inference(resolution,[],[f66,f53])).
1.13/0.66	tff(f66,plain,(
1.13/0.66	  ( ! [X2 : set,X0 : element,X1 : set] : (~member(X0,intersection(X1,X2)) | member(X0,X2)) )),
1.13/0.66	  inference(cnf_transformation,[],[f42])).
1.13/0.66	tff(f1587,plain,(
1.13/0.66	  spl4_13 | spl4_2),
1.13/0.66	  inference(avatar_split_clause,[],[f1558,f84,f1584])).
1.13/0.66	tff(f1558,plain,(
1.13/0.66	  empty_set = intersection(sK1,singleton(sK0)) | spl4_2),
1.13/0.66	  inference(resolution,[],[f291,f86])).
1.13/0.66	tff(f291,plain,(
1.13/0.66	  ( ! [X0 : set,X1 : element] : (member(X1,X0) | empty_set = intersection(X0,singleton(X1))) )),
1.13/0.66	  inference(duplicate_literal_removal,[],[f286])).
1.13/0.66	tff(f286,plain,(
1.13/0.66	  ( ! [X0 : set,X1 : element] : (member(X1,X0) | empty_set = intersection(X0,singleton(X1)) | empty_set = intersection(X0,singleton(X1))) )),
1.13/0.66	  inference(superposition,[],[f121,f158])).
1.13/0.66	tff(f158,plain,(
1.13/0.66	  ( ! [X4 : set,X5 : element] : (sK3(intersection(X4,singleton(X5))) = X5 | empty_set = intersection(X4,singleton(X5))) )),
1.13/0.66	  inference(resolution,[],[f116,f56])).
1.13/0.66	tff(f998,plain,(
1.13/0.66	  spl4_11 | spl4_12 | ~spl4_4 | ~spl4_8),
1.13/0.66	  inference(avatar_split_clause,[],[f980,f267,f94,f995,f992])).
1.13/0.66	tff(f992,plain,(
1.13/0.66	  spl4_11 <=> ! [X0 : element] : empty_set != singleton(X0)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_11])])).
1.13/0.66	tff(f995,plain,(
1.13/0.66	  spl4_12 <=> 1 = cardinality(empty_set)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_12])])).
1.13/0.66	tff(f94,plain,(
1.13/0.66	  spl4_4 <=> 0 = cardinality(empty_set)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_4])])).
1.13/0.66	tff(f267,plain,(
1.13/0.66	  spl4_8 <=> empty_set = union(empty_set,empty_set)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_8])])).
1.13/0.66	tff(f980,plain,(
1.13/0.66	  ( ! [X0 : element] : (1 = cardinality(empty_set) | empty_set != singleton(X0)) ) | (~spl4_4 | ~spl4_8)),
1.13/0.66	  inference(constrained_superposition,[],[f180,f269])).
1.13/0.66	tff(f269,plain,(
1.13/0.66	  empty_set = union(empty_set,empty_set) | ~spl4_8),
1.13/0.66	  inference(avatar_component_clause,[],[f267])).
1.13/0.66	tff(f180,plain,(
1.13/0.66	  ( ! [X9 : element] : (1 = cardinality(union(singleton(X9),empty_set))) ) | ~spl4_4),
1.13/0.66	  inference(evaluation,[],[f179])).
1.13/0.66	tff(f179,plain,(
1.13/0.66	  ( ! [X9 : element] : (cardinality(union(singleton(X9),empty_set)) = $sum(0,1)) ) | ~spl4_4),
1.13/0.66	  inference(forward_demodulation,[],[f174,f96])).
1.13/0.66	tff(f96,plain,(
1.13/0.66	  0 = cardinality(empty_set) | ~spl4_4),
1.13/0.66	  inference(avatar_component_clause,[],[f94])).
1.13/0.66	tff(f174,plain,(
1.13/0.66	  ( ! [X9 : element] : (cardinality(union(singleton(X9),empty_set)) = $sum(cardinality(empty_set),1)) )),
1.13/0.66	  inference(trivial_inequality_removal,[],[f172])).
1.13/0.66	tff(f172,plain,(
1.13/0.66	  ( ! [X9 : element] : (empty_set != empty_set | cardinality(union(singleton(X9),empty_set)) = $sum(cardinality(empty_set),1)) )),
1.13/0.66	  inference(superposition,[],[f65,f157])).
1.13/0.66	tff(f157,plain,(
1.13/0.66	  ( ! [X3 : set] : (empty_set = intersection(X3,empty_set)) )),
1.13/0.66	  inference(resolution,[],[f116,f76])).
1.13/0.66	tff(f76,plain,(
1.13/0.66	  ( ! [X2 : element] : (~member(X2,empty_set)) )),
1.13/0.66	  inference(equality_resolution,[],[f52])).
1.13/0.66	tff(f52,plain,(
1.13/0.66	  ( ! [X2 : element,X0 : set] : (~member(X2,X0) | empty_set != X0) )),
1.13/0.66	  inference(cnf_transformation,[],[f34])).
1.13/0.66	tff(f969,plain,(
1.13/0.66	  ~spl4_9 | spl4_10 | ~spl4_7),
1.13/0.66	  inference(avatar_split_clause,[],[f935,f253,f967,f963])).
1.13/0.66	tff(f967,plain,(
1.13/0.66	  spl4_10 <=> ! [X0 : set] : empty_set = difference(X0,empty_set)),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_10])])).
1.13/0.66	tff(f253,plain,(
1.13/0.66	  spl4_7 <=> empty_set = complement(complement(empty_set))),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_7])])).
1.13/0.66	tff(f935,plain,(
1.13/0.66	  ( ! [X0 : set] : (empty_set = difference(X0,empty_set) | empty_set != complement(empty_set)) ) | ~spl4_7),
1.13/0.66	  inference(constrained_superposition,[],[f348,f255])).
1.13/0.66	tff(f255,plain,(
1.13/0.66	  empty_set = complement(complement(empty_set)) | ~spl4_7),
1.13/0.66	  inference(avatar_component_clause,[],[f253])).
1.13/0.66	tff(f348,plain,(
1.13/0.66	  ( ! [X1 : set] : (empty_set = difference(X1,complement(empty_set))) )),
1.13/0.66	  inference(resolution,[],[f208,f76])).
1.13/0.66	tff(f208,plain,(
1.13/0.66	  ( ! [X14 : set,X13 : set] : (member(sK3(difference(X13,complement(X14))),X14) | empty_set = difference(X13,complement(X14))) )),
1.13/0.66	  inference(resolution,[],[f123,f54])).
1.13/0.66	tff(f54,plain,(
1.13/0.66	  ( ! [X0 : element,X1 : set] : (member(X0,complement(X1)) | member(X0,X1)) )),
1.13/0.66	  inference(cnf_transformation,[],[f35])).
1.13/0.66	tff(f123,plain,(
1.13/0.66	  ( ! [X0 : set,X1 : set] : (~member(sK3(difference(X0,X1)),X1) | empty_set = difference(X0,X1)) )),
1.13/0.66	  inference(resolution,[],[f71,f53])).
1.13/0.66	tff(f71,plain,(
1.13/0.66	  ( ! [X2 : set,X0 : element,X1 : set] : (~member(X0,difference(X2,X1)) | ~member(X0,X1)) )),
1.13/0.66	  inference(cnf_transformation,[],[f44])).
1.13/0.66	tff(f44,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : (((~member(X0,X1) & member(X0,X2)) | ~member(X0,difference(X2,X1))) & (member(X0,difference(X2,X1)) | member(X0,X1) | ~member(X0,X2)))),
1.13/0.66	  inference(flattening,[],[f43])).
1.13/0.66	tff(f43,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : (((~member(X0,X1) & member(X0,X2)) | ~member(X0,difference(X2,X1))) & (member(X0,difference(X2,X1)) | (member(X0,X1) | ~member(X0,X2))))),
1.13/0.66	  inference(nnf_transformation,[],[f24])).
1.13/0.66	tff(f24,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : ((~member(X0,X1) & member(X0,X2)) <=> member(X0,difference(X2,X1)))),
1.13/0.66	  inference(rectify,[],[f6])).
1.13/0.66	tff(f6,axiom,(
1.13/0.66	  ! [X1 : element,X0 : set,X6 : set] : ((~member(X1,X0) & member(X1,X6)) <=> member(X1,difference(X6,X0)))),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference)).
1.13/0.66	tff(f270,plain,(
1.13/0.66	  spl4_8),
1.13/0.66	  inference(avatar_split_clause,[],[f257,f267])).
1.13/0.66	tff(f257,plain,(
1.13/0.66	  empty_set = union(empty_set,empty_set)),
1.13/0.66	  inference(resolution,[],[f212,f76])).
1.13/0.66	tff(f212,plain,(
1.13/0.66	  ( ! [X0 : set] : (member(sK3(union(X0,empty_set)),X0) | empty_set = union(X0,empty_set)) )),
1.13/0.66	  inference(resolution,[],[f131,f76])).
1.13/0.66	tff(f131,plain,(
1.13/0.66	  ( ! [X6 : set,X7 : set] : (member(sK3(union(X6,X7)),X7) | member(sK3(union(X6,X7)),X6) | empty_set = union(X6,X7)) )),
1.13/0.66	  inference(resolution,[],[f74,f53])).
1.13/0.66	tff(f74,plain,(
1.13/0.66	  ( ! [X2 : set,X0 : element,X1 : set] : (~member(X0,union(X1,X2)) | member(X0,X1) | member(X0,X2)) )),
1.13/0.66	  inference(cnf_transformation,[],[f46])).
1.13/0.66	tff(f46,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : ((member(X0,X2) | member(X0,X1) | ~member(X0,union(X1,X2))) & (member(X0,union(X1,X2)) | (~member(X0,X2) & ~member(X0,X1))))),
1.13/0.66	  inference(flattening,[],[f45])).
1.13/0.66	tff(f45,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : (((member(X0,X2) | member(X0,X1)) | ~member(X0,union(X1,X2))) & (member(X0,union(X1,X2)) | (~member(X0,X2) & ~member(X0,X1))))),
1.13/0.66	  inference(nnf_transformation,[],[f25])).
1.13/0.66	tff(f25,plain,(
1.13/0.66	  ! [X0 : element,X1 : set,X2 : set] : ((member(X0,X2) | member(X0,X1)) <=> member(X0,union(X1,X2)))),
1.13/0.66	  inference(rectify,[],[f8])).
1.13/0.66	tff(f8,axiom,(
1.13/0.66	  ! [X2 : element,X0 : set,X1 : set] : ((member(X2,X1) | member(X2,X0)) <=> member(X2,union(X0,X1)))),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union)).
1.13/0.66	tff(f256,plain,(
1.13/0.66	  spl4_7),
1.13/0.66	  inference(avatar_split_clause,[],[f243,f253])).
1.13/0.66	tff(f243,plain,(
1.13/0.66	  empty_set = complement(complement(empty_set))),
1.13/0.66	  inference(resolution,[],[f136,f76])).
1.13/0.66	tff(f136,plain,(
1.13/0.66	  ( ! [X8 : set] : (member(sK3(complement(complement(X8))),X8) | empty_set = complement(complement(X8))) )),
1.13/0.66	  inference(resolution,[],[f113,f54])).
1.13/0.66	tff(f110,plain,(
1.13/0.66	  spl4_5 | ~spl4_6 | ~spl4_3),
1.13/0.66	  inference(avatar_split_clause,[],[f99,f89,f107,f103])).
1.13/0.66	tff(f103,plain,(
1.13/0.66	  spl4_5 <=> empty_set = sK1),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_5])])).
1.13/0.66	tff(f107,plain,(
1.13/0.66	  spl4_6 <=> 0 = sK2),
1.13/0.66	  introduced(avatar_definition,[new_symbols(naming,[spl4_6])])).
1.13/0.66	tff(f99,plain,(
1.13/0.66	  0 != sK2 | empty_set = sK1 | ~spl4_3),
1.13/0.66	  inference(superposition,[],[f51,f91])).
1.13/0.66	tff(f51,plain,(
1.13/0.66	  ( ! [X0 : set] : (cardinality(X0) != 0 | empty_set = X0) )),
1.13/0.66	  inference(cnf_transformation,[],[f30])).
1.13/0.66	tff(f30,plain,(
1.13/0.66	  ! [X0 : set] : ((empty_set = X0 | cardinality(X0) != 0) & (cardinality(X0) = 0 | empty_set != X0))),
1.13/0.66	  inference(nnf_transformation,[],[f16])).
1.13/0.66	tff(f16,plain,(
1.13/0.66	  ! [X0 : set] : (empty_set = X0 <=> cardinality(X0) = 0)),
1.13/0.66	  inference(rectify,[],[f14])).
1.13/0.66	tff(f14,axiom,(
1.13/0.66	  ! [X5 : set] : (empty_set = X5 <=> cardinality(X5) = 0)),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cardinality_empty_set)).
1.13/0.66	tff(f97,plain,(
1.13/0.66	  spl4_4),
1.13/0.66	  inference(avatar_split_clause,[],[f75,f94])).
1.13/0.66	tff(f75,plain,(
1.13/0.66	  0 = cardinality(empty_set)),
1.13/0.66	  inference(equality_resolution,[],[f50])).
1.13/0.66	tff(f50,plain,(
1.13/0.66	  ( ! [X0 : set] : (cardinality(X0) = 0 | empty_set != X0) )),
1.13/0.66	  inference(cnf_transformation,[],[f30])).
1.13/0.66	tff(f92,plain,(
1.13/0.66	  spl4_3),
1.13/0.66	  inference(avatar_split_clause,[],[f47,f89])).
1.13/0.66	tff(f47,plain,(
1.13/0.66	  sK2 = cardinality(sK1)),
1.13/0.66	  inference(cnf_transformation,[],[f29])).
1.13/0.66	tff(f29,plain,(
1.13/0.66	  $sum(sK2,1) != cardinality(union(singleton(sK0),sK1)) & ~member(sK0,sK1) & sK2 = cardinality(sK1)),
1.13/0.66	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f28])).
1.13/0.66	tff(f28,plain,(
1.13/0.66	  ? [X0 : element,X1 : set,X2 : $int] : ($sum(X2,1) != cardinality(union(singleton(X0),X1)) & ~member(X0,X1) & cardinality(X1) = X2) => ($sum(sK2,1) != cardinality(union(singleton(sK0),sK1)) & ~member(sK0,sK1) & sK2 = cardinality(sK1))),
1.13/0.66	  introduced(choice_axiom,[])).
1.13/0.66	tff(f27,plain,(
1.13/0.66	  ? [X0 : element,X1 : set,X2 : $int] : ($sum(X2,1) != cardinality(union(singleton(X0),X1)) & ~member(X0,X1) & cardinality(X1) = X2)),
1.13/0.66	  inference(flattening,[],[f26])).
1.13/0.66	tff(f26,plain,(
1.13/0.66	  ? [X0 : element,X1 : set,X2 : $int] : ($sum(X2,1) != cardinality(union(singleton(X0),X1)) & (~member(X0,X1) & cardinality(X1) = X2))),
1.13/0.66	  inference(ennf_transformation,[],[f15])).
1.13/0.66	tff(f15,plain,(
1.13/0.66	  ~! [X0 : element,X1 : set,X2 : $int] : ((~member(X0,X1) & cardinality(X1) = X2) => $sum(X2,1) = cardinality(union(singleton(X0),X1)))),
1.13/0.66	  inference(rectify,[],[f3])).
1.13/0.66	tff(f3,negated_conjecture,(
1.13/0.66	  ~! [X2 : element,X3 : set,X4 : $int] : ((~member(X2,X3) & cardinality(X3) = X4) => $sum(X4,1) = cardinality(union(singleton(X2),X3)))),
1.13/0.66	  inference(negated_conjecture,[],[f2])).
1.13/0.66	tff(f2,conjecture,(
1.13/0.66	  ! [X2 : element,X3 : set,X4 : $int] : ((~member(X2,X3) & cardinality(X3) = X4) => $sum(X4,1) = cardinality(union(singleton(X2),X3)))),
1.13/0.66	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vc2)).
1.13/0.66	tff(f87,plain,(
1.13/0.66	  ~spl4_2),
1.13/0.66	  inference(avatar_split_clause,[],[f48,f84])).
1.13/0.66	tff(f48,plain,(
1.13/0.66	  ~member(sK0,sK1)),
1.13/0.66	  inference(cnf_transformation,[],[f29])).
1.13/0.66	tff(f82,plain,(
1.13/0.66	  ~spl4_1),
1.13/0.66	  inference(avatar_split_clause,[],[f49,f79])).
1.13/0.66	tff(f49,plain,(
1.13/0.66	  $sum(sK2,1) != cardinality(union(singleton(sK0),sK1))),
1.13/0.66	  inference(cnf_transformation,[],[f29])).
1.13/0.66	% SZS output end Proof for theBenchmark
1.13/0.66	% (7192)------------------------------
1.13/0.66	% (7192)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
1.13/0.66	% (7192)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
1.13/0.66	% (7192)Termination reason: Refutation
1.13/0.66	
1.13/0.66	% (7192)Memory used [KB]: 2686
1.13/0.66	% (7192)Time elapsed: 0.111 s
1.13/0.66	% (7192)------------------------------
1.13/0.66	% (7192)------------------------------
1.13/0.66	% (7188)Success in time 0.17 s
1.13/0.66	% Vampire---4.8 exiting
1.13/0.66	EOF