TSTP Solution File: SEU327+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU327+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 : n027.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 0.20s 0.44s
% Output : Refutation 0.20s
% 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(f1777,plain,
$false,
inference(trivial_inequality_removal,[],[f1776]) ).
fof(f1776,plain,
empty_set != empty_set,
inference(superposition,[],[f144,f1301]) ).
fof(f1301,plain,
empty_set = sK4,
inference(trivial_inequality_removal,[],[f1299]) ).
fof(f1299,plain,
( set_difference(sK3,union(sK4)) != set_difference(sK3,union(sK4))
| empty_set = sK4 ),
inference(superposition,[],[f559,f1297]) ).
fof(f1297,plain,
( meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = set_difference(sK3,union(sK4))
| empty_set = sK4 ),
inference(backward_demodulation,[],[f667,f1293]) ).
fof(f1293,plain,
set_difference(sK3,union(sK4)) = subset_difference(sK3,sK3,union(sK4)),
inference(resolution,[],[f1279,f143]) ).
fof(f143,plain,
element(sK4,powerset(powerset(sK3))),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,union_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] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,union_of_subsets(X0,X1))
& empty_set != X1
& element(X1,powerset(powerset(X0))) )
=> ( meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,union_of_subsets(sK3,sK4))
& empty_set != sK4
& element(sK4,powerset(powerset(sK3))) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,union_of_subsets(X0,X1))
& empty_set != X1
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
? [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,union_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
=> meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,union_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,union_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tops_2) ).
fof(f1279,plain,
( ~ element(sK4,powerset(powerset(sK3)))
| set_difference(sK3,union(sK4)) = subset_difference(sK3,sK3,union(sK4)) ),
inference(resolution,[],[f592,f501]) ).
fof(f501,plain,
( element(union(sK4),powerset(sK3))
| ~ element(sK4,powerset(powerset(sK3))) ),
inference(superposition,[],[f214,f430]) ).
fof(f430,plain,
union_of_subsets(sK3,sK4) = union(sK4),
inference(resolution,[],[f212,f143]) ).
fof(f212,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f214,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_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,
( meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = subset_difference(sK3,sK3,union(sK4))
| empty_set = sK4 ),
inference(forward_demodulation,[],[f663,f430]) ).
fof(f663,plain,
( empty_set = sK4
| meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) = subset_difference(sK3,sK3,union_of_subsets(sK3,sK4)) ),
inference(resolution,[],[f233,f143]) ).
fof(f233,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1)) ),
inference(forward_demodulation,[],[f218,f153]) ).
fof(f218,plain,
! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_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
=> meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f559,plain,
meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != set_difference(sK3,union(sK4)),
inference(backward_demodulation,[],[f433,f555]) ).
fof(f555,plain,
subset_complement(sK3,union(sK4)) = set_difference(sK3,union(sK4)),
inference(resolution,[],[f526,f143]) ).
fof(f526,plain,
( ~ element(sK4,powerset(powerset(sK3)))
| subset_complement(sK3,union(sK4)) = set_difference(sK3,union(sK4)) ),
inference(resolution,[],[f501,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(f433,plain,
meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,union(sK4)),
inference(backward_demodulation,[],[f145,f430]) ).
fof(f145,plain,
meet_of_subsets(sK3,complements_of_subsets(sK3,sK4)) != subset_complement(sK3,union_of_subsets(sK3,sK4)),
inference(cnf_transformation,[],[f129]) ).
fof(f144,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n027.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 : Fri May 3 11:41:36 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (32047)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (32050)WARNING: value z3 for option sas not known
% 0.14/0.37 % (32053)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)
% 0.14/0.38 % (32051)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (32050)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)
% 0.14/0.38 % (32048)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (32052)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)
% 0.14/0.38 % (32049)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (32054)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [4]
% 0.14/0.41 TRYING [3]
% 0.20/0.42 TRYING [5]
% 0.20/0.44 % (32053)First to succeed.
% 0.20/0.44 % (32053)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-32047"
% 0.20/0.44 % (32053)Refutation found. Thanks to Tanya!
% 0.20/0.44 % SZS status Theorem for theBenchmark
% 0.20/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.44 % (32053)------------------------------
% 0.20/0.44 % (32053)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.44 % (32053)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (32053)Memory used [KB]: 1656
% 0.20/0.44 % (32053)Time elapsed: 0.069 s
% 0.20/0.44 % (32053)Instructions burned: 137 (million)
% 0.20/0.44 % (32047)Success in time 0.085 s
%------------------------------------------------------------------------------