TSTP Solution File: SEU328+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU328+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -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 : Sun May 5 09:33:43 EDT 2024
% Result : Theorem 0.17s 0.42s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% Number of atoms : 98 ( 56 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 40 ~; 28 |; 11 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 57 ( 51 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1781,plain,
$false,
inference(trivial_inequality_removal,[],[f1780]) ).
fof(f1780,plain,
empty_set != empty_set,
inference(superposition,[],[f144,f1306]) ).
fof(f1306,plain,
empty_set = sK4,
inference(trivial_inequality_removal,[],[f1304]) ).
fof(f1304,plain,
( set_difference(sK3,set_meet(sK4)) != set_difference(sK3,set_meet(sK4))
| empty_set = sK4 ),
inference(superposition,[],[f688,f1302]) ).
fof(f1302,plain,
( union_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = set_difference(sK3,set_meet(sK4))
| empty_set = sK4 ),
inference(backward_demodulation,[],[f667,f1298]) ).
fof(f1298,plain,
set_difference(sK3,set_meet(sK4)) = subset_difference(sK3,sK3,set_meet(sK4)),
inference(resolution,[],[f1282,f143]) ).
fof(f143,plain,
element(sK4,powerset(powerset(sK3))),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( union_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,meet_of_subsets(sK3,sK4))
& empty_set != sK4
& element(sK4,powerset(powerset(sK3))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f79,f128]) ).
fof(f128,plain,
( ? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1))
& empty_set != X1
& element(X1,powerset(powerset(X0))) )
=> ( union_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,meet_of_subsets(sK3,sK4))
& empty_set != sK4
& element(sK4,powerset(powerset(sK3))) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1))
& empty_set != X1
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1))
& empty_set != X1
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
fof(f1282,plain,
( ~ element(sK4,powerset(powerset(sK3)))
| set_difference(sK3,set_meet(sK4)) = subset_difference(sK3,sK3,set_meet(sK4)) ),
inference(resolution,[],[f592,f512]) ).
fof(f512,plain,
( element(set_meet(sK4),powerset(sK3))
| ~ element(sK4,powerset(powerset(sK3))) ),
inference(superposition,[],[f215,f475]) ).
fof(f475,plain,
meet_of_subsets(sK3,sK4) = set_meet(sK4),
inference(resolution,[],[f213,f143]) ).
fof(f213,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| meet_of_subsets(X0,X1) = set_meet(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f215,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f592,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_difference(X0,X0,X1) ),
inference(resolution,[],[f224,f232]) ).
fof(f232,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[],[f156,f153]) ).
fof(f153,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f156,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f224,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f667,plain,
( union_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = subset_difference(sK3,sK3,set_meet(sK4))
| empty_set = sK4 ),
inference(forward_demodulation,[],[f663,f475]) ).
fof(f663,plain,
( empty_set = sK4
| union_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = subset_difference(sK3,sK3,meet_of_subsets(sK3,sK4)) ),
inference(resolution,[],[f233,f143]) ).
fof(f233,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1)) ),
inference(forward_demodulation,[],[f218,f153]) ).
fof(f218,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f688,plain,
union_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != set_difference(sK3,set_meet(sK4)),
inference(backward_demodulation,[],[f478,f684]) ).
fof(f684,plain,
subset_complement(sK3,set_meet(sK4)) = set_difference(sK3,set_meet(sK4)),
inference(resolution,[],[f528,f143]) ).
fof(f528,plain,
( ~ element(sK4,powerset(powerset(sK3)))
| subset_complement(sK3,set_meet(sK4)) = set_difference(sK3,set_meet(sK4)) ),
inference(resolution,[],[f512,f210]) ).
fof(f210,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f478,plain,
union_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,set_meet(sK4)),
inference(backward_demodulation,[],[f145,f475]) ).
fof(f145,plain,
union_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,meet_of_subsets(sK3,sK4)),
inference(cnf_transformation,[],[f129]) ).
fof(f144,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU328+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n021.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 : Fri May 3 11:27:58 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (13260)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (13261)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35 % (13267)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 theBenchmark for (497ds/0Mi)
% 0.11/0.35 % (13263)WARNING: value z3 for option sas not known
% 0.11/0.35 % (13264)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35 % (13266)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 theBenchmark for (522ds/0Mi)
% 0.11/0.35 % (13262)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35 % (13263)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 theBenchmark for (569ds/0Mi)
% 0.11/0.35 % (13265)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 theBenchmark for (531ds/0Mi)
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.36 TRYING [1]
% 0.11/0.36 TRYING [2]
% 0.11/0.36 TRYING [4]
% 0.11/0.38 TRYING [3]
% 0.11/0.39 TRYING [5]
% 0.17/0.41 TRYING [4]
% 0.17/0.42 % (13266)First to succeed.
% 0.17/0.42 % (13266)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13260"
% 0.17/0.42 % (13266)Refutation found. Thanks to Tanya!
% 0.17/0.42 % SZS status Theorem for theBenchmark
% 0.17/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.42 % (13266)------------------------------
% 0.17/0.42 % (13266)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.42 % (13266)Termination reason: Refutation
% 0.17/0.42
% 0.17/0.42 % (13266)Memory used [KB]: 1656
% 0.17/0.42 % (13266)Time elapsed: 0.072 s
% 0.17/0.42 % (13266)Instructions burned: 138 (million)
% 0.17/0.42 % (13260)Success in time 0.077 s
%------------------------------------------------------------------------------