%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU176+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:47:35 PM UTC 2026
% Result : Theorem 10.49s 2.38s
% Output : Refutation 11.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 105 ( 40 unt; 2 def)
% Number of atoms : 192 ( 95 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 160 ( 73 ~; 61 |; 8 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 106 ( 0 sgn 102 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f20,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(f29,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f38,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(f39,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(f41,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f51,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f52,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f70,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(f71,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(f72,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f108,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f110,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f111,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> 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(f112,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f111]) ).
fof(f133,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f149,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f152,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f38]) ).
fof(f153,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f39]) ).
fof(f156,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f41]) ).
fof(f159,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f51]) ).
fof(f160,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f52]) ).
fof(f170,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f70]) ).
fof(f171,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f71]) ).
fof(f172,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f72]) ).
fof(f173,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f172]) ).
fof(f198,plain,
! [X0,X1] :
( empty_set = X1
| empty_set != complements_of_subsets(X0,X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f108]) ).
fof(f199,plain,
! [X0,X1] :
( empty_set = X1
| empty_set != complements_of_subsets(X0,X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f198]) ).
fof(f201,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f110]) ).
fof(f202,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f201]) ).
fof(f203,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
& X1 != empty_set
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f112]) ).
fof(f204,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
& X1 != empty_set
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f203]) ).
fof(f300,plain,
( union_of_subsets(sK29,complements_of_subsets(sK29,sK30)) != subset_difference(sK29,cast_to_subset(sK29),meet_of_subsets(sK29,sK30))
& empty_set != sK30
& element(sK30,powerset(powerset(sK29))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29,sK30]),skolemize(X0,sK29),skolemize(X1,sK30)],[f204]) ).
fof(f364,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f17]) ).
fof(f377,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
fof(f389,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f391,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(union_of_subsets(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f152]) ).
fof(f392,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f153]) ).
fof(f394,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f156]) ).
fof(f403,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f159]) ).
fof(f404,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f160]) ).
fof(f431,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f432,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| meet_of_subsets(X0,X1) = set_meet(X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f433,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f173]) ).
fof(f487,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f199]) ).
fof(f489,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f490,plain,
element(sK30,powerset(powerset(sK29))),
inference(cnf_transformation,[],[f300]) ).
fof(f491,plain,
empty_set != sK30,
inference(cnf_transformation,[],[f300]) ).
fof(f492,plain,
union_of_subsets(sK29,complements_of_subsets(sK29,sK30)) != subset_difference(sK29,cast_to_subset(sK29),meet_of_subsets(sK29,sK30)),
inference(cnf_transformation,[],[f300]) ).
fof(f516,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f133]) ).
fof(f628,plain,
! [X0,X1] :
( empty_set = complements_of_subsets(X0,X1)
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,complements_of_subsets(X0,X1))) = meet_of_subsets(X0,complements_of_subsets(X0,complements_of_subsets(X0,X1)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(resolution,[],[f489,f394]) ).
fof(f629,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = complements_of_subsets(X0,X1)
| meet_of_subsets(X0,complements_of_subsets(X0,complements_of_subsets(X0,X1))) = subset_difference(X0,X0,union_of_subsets(X0,complements_of_subsets(X0,X1))) ),
inference(forward_demodulation,[],[f628,f364]) ).
fof(f631,plain,
sK30 = complements_of_subsets(sK29,complements_of_subsets(sK29,sK30)),
inference(resolution,[],[f490,f404]) ).
fof(f641,plain,
meet_of_subsets(sK29,sK30) = set_meet(sK30),
inference(resolution,[],[f432,f490]) ).
fof(f643,plain,
union_of_subsets(sK29,complements_of_subsets(sK29,sK30)) != subset_difference(sK29,cast_to_subset(sK29),set_meet(sK30)),
inference(superposition,[],[f492,f641]) ).
fof(f644,plain,
( element(set_meet(sK30),powerset(sK29))
| ~ element(sK30,powerset(powerset(sK29))) ),
inference(superposition,[],[f392,f641]) ).
fof(f645,plain,
element(set_meet(sK30),powerset(sK29)),
inference(forward_subsumption_resolution,[],[f644,f490]) ).
fof(f646,plain,
union_of_subsets(sK29,complements_of_subsets(sK29,sK30)) != subset_difference(sK29,sK29,set_meet(sK30)),
inference(forward_demodulation,[],[f643,f364]) ).
fof(f647,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = union(complements_of_subsets(X0,X1)) ),
inference(resolution,[],[f431,f394]) ).
fof(f651,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(union_of_subsets(X0,complements_of_subsets(X0,X1)),powerset(X0)) ),
inference(resolution,[],[f391,f394]) ).
fof(f655,plain,
! [X0] : element(union_of_subsets(X0,cast_to_subset(powerset(X0))),powerset(X0)),
inference(resolution,[],[f389,f391]) ).
fof(f656,plain,
! [X0] : union_of_subsets(X0,cast_to_subset(powerset(X0))) = union(cast_to_subset(powerset(X0))),
inference(resolution,[],[f389,f431]) ).
fof(f663,plain,
! [X0] : union(powerset(X0)) = union_of_subsets(X0,powerset(X0)),
inference(forward_demodulation,[],[f656,f364]) ).
fof(f664,plain,
! [X0] : element(union_of_subsets(X0,powerset(X0)),powerset(X0)),
inference(forward_demodulation,[],[f655,f364]) ).
fof(f666,plain,
! [X0] : union_of_subsets(X0,powerset(X0)) = X0,
inference(forward_demodulation,[],[f663,f516]) ).
fof(f679,plain,
! [X0] :
( ~ element(X0,powerset(sK29))
| subset_difference(sK29,X0,set_meet(sK30)) = set_difference(X0,set_meet(sK30)) ),
inference(resolution,[],[f433,f645]) ).
fof(f693,plain,
element(union_of_subsets(sK29,complements_of_subsets(sK29,sK30)),powerset(sK29)),
inference(resolution,[],[f651,f490]) ).
fof(f697,plain,
! [X0] :
( ~ element(X0,powerset(sK29))
| subset_difference(sK29,X0,union_of_subsets(sK29,complements_of_subsets(sK29,sK30))) = set_difference(X0,union_of_subsets(sK29,complements_of_subsets(sK29,sK30))) ),
inference(resolution,[],[f693,f433]) ).
fof(f700,plain,
union_of_subsets(sK29,complements_of_subsets(sK29,sK30)) = union(complements_of_subsets(sK29,sK30)),
inference(resolution,[],[f647,f490]) ).
fof(f717,plain,
! [X0] : element(X0,powerset(X0)),
inference(superposition,[],[f664,f666]) ).
fof(f770,plain,
union_of_subsets(sK29,complements_of_subsets(sK29,sK30)) = subset_complement(sK29,subset_complement(sK29,union_of_subsets(sK29,complements_of_subsets(sK29,sK30)))),
inference(resolution,[],[f403,f693]) ).
fof(f772,plain,
union(complements_of_subsets(sK29,sK30)) = subset_complement(sK29,subset_complement(sK29,union(complements_of_subsets(sK29,sK30)))),
inference(forward_demodulation,[],[f770,f700]) ).
fof(f797,plain,
( empty_set = complements_of_subsets(sK29,sK30)
| meet_of_subsets(sK29,complements_of_subsets(sK29,complements_of_subsets(sK29,sK30))) = subset_difference(sK29,sK29,union_of_subsets(sK29,complements_of_subsets(sK29,sK30))) ),
inference(resolution,[],[f629,f490]) ).
fof(f805,plain,
( meet_of_subsets(sK29,complements_of_subsets(sK29,complements_of_subsets(sK29,sK30))) = subset_difference(sK29,sK29,union(complements_of_subsets(sK29,sK30)))
| empty_set = complements_of_subsets(sK29,sK30) ),
inference(forward_demodulation,[],[f797,f700]) ).
fof(f809,plain,
( meet_of_subsets(sK29,sK30) = subset_difference(sK29,sK29,union(complements_of_subsets(sK29,sK30)))
| empty_set = complements_of_subsets(sK29,sK30) ),
inference(forward_demodulation,[],[f805,f631]) ).
fof(f813,plain,
( set_meet(sK30) = subset_difference(sK29,sK29,union(complements_of_subsets(sK29,sK30)))
| empty_set = complements_of_subsets(sK29,sK30) ),
inference(forward_demodulation,[],[f809,f641]) ).
fof(f817,definition,
( spl34_5
<=> empty_set = complements_of_subsets(sK29,sK30) ),
introduced(definition,[new_symbols(definition,[spl34_5])],[avatar_definition]) ).
fof(f818,plain,
( empty_set = complements_of_subsets(sK29,sK30)
| ~ spl34_5 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f820,definition,
( spl34_6
<=> set_meet(sK30) = subset_difference(sK29,sK29,union(complements_of_subsets(sK29,sK30))) ),
introduced(definition,[new_symbols(definition,[spl34_6])],[avatar_definition]) ).
fof(f821,plain,
( set_meet(sK30) = subset_difference(sK29,sK29,union(complements_of_subsets(sK29,sK30)))
| ~ spl34_6 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f822,plain,
( spl34_5
| spl34_6 ),
inference(avatar_split_clause,[],[f813,f820,f817]) ).
fof(f832,plain,
( empty_set != empty_set
| empty_set = sK30
| ~ element(sK30,powerset(powerset(sK29)))
| ~ spl34_5 ),
inference(superposition,[],[f487,f818]) ).
fof(f834,plain,
( empty_set = sK30
| ~ element(sK30,powerset(powerset(sK29)))
| ~ spl34_5 ),
inference(trivial_inequality_removal,[],[f832]) ).
fof(f837,plain,
( ~ element(sK30,powerset(powerset(sK29)))
| ~ spl34_5 ),
inference(forward_subsumption_resolution,[],[f834,f491]) ).
fof(f839,plain,
( $false
| ~ spl34_5 ),
inference(forward_subsumption_resolution,[],[f837,f490]) ).
fof(f840,plain,
~ spl34_5,
inference(avatar_contradiction_clause,[],[f839]) ).
fof(f936,plain,
subset_complement(sK29,set_meet(sK30)) = set_difference(sK29,set_meet(sK30)),
inference(resolution,[],[f377,f645]) ).
fof(f938,plain,
subset_complement(sK29,union_of_subsets(sK29,complements_of_subsets(sK29,sK30))) = set_difference(sK29,union_of_subsets(sK29,complements_of_subsets(sK29,sK30))),
inference(resolution,[],[f377,f693]) ).
fof(f940,plain,
subset_complement(sK29,union(complements_of_subsets(sK29,sK30))) = set_difference(sK29,union(complements_of_subsets(sK29,sK30))),
inference(forward_demodulation,[],[f938,f700]) ).
fof(f3487,plain,
subset_difference(sK29,sK29,set_meet(sK30)) = set_difference(sK29,set_meet(sK30)),
inference(resolution,[],[f679,f717]) ).
fof(f3500,plain,
subset_difference(sK29,sK29,set_meet(sK30)) = subset_complement(sK29,set_meet(sK30)),
inference(forward_demodulation,[],[f3487,f936]) ).
fof(f4038,plain,
subset_difference(sK29,sK29,union_of_subsets(sK29,complements_of_subsets(sK29,sK30))) = set_difference(sK29,union_of_subsets(sK29,complements_of_subsets(sK29,sK30))),
inference(resolution,[],[f697,f717]) ).
fof(f4049,plain,
subset_difference(sK29,sK29,union(complements_of_subsets(sK29,sK30))) = set_difference(sK29,union(complements_of_subsets(sK29,sK30))),
inference(forward_demodulation,[],[f4038,f700]) ).
fof(f4060,plain,
subset_complement(sK29,union(complements_of_subsets(sK29,sK30))) = subset_difference(sK29,sK29,union(complements_of_subsets(sK29,sK30))),
inference(forward_demodulation,[],[f4049,f940]) ).
fof(f4067,plain,
( set_meet(sK30) = subset_complement(sK29,union(complements_of_subsets(sK29,sK30)))
| ~ spl34_6 ),
inference(forward_demodulation,[],[f4060,f821]) ).
fof(f4072,plain,
( union(complements_of_subsets(sK29,sK30)) = subset_complement(sK29,set_meet(sK30))
| ~ spl34_6 ),
inference(superposition,[],[f772,f4067]) ).
fof(f5488,plain,
union_of_subsets(sK29,complements_of_subsets(sK29,sK30)) != subset_complement(sK29,set_meet(sK30)),
inference(superposition,[],[f646,f3500]) ).
fof(f5489,plain,
union(complements_of_subsets(sK29,sK30)) != subset_complement(sK29,set_meet(sK30)),
inference(forward_demodulation,[],[f5488,f700]) ).
fof(f5490,plain,
( $false
| ~ spl34_6 ),
inference(forward_subsumption_resolution,[],[f5489,f4072]) ).
fof(f5491,plain,
~ spl34_6,
inference(avatar_contradiction_clause,[],[f5490]) ).
cnf(s5,plain,
( spl34_5
| spl34_6 ),
inference(sat_conversion,[],[f822]) ).
cnf(s7,plain,
~ spl34_5,
inference(sat_conversion,[],[f840]) ).
cnf(s225,plain,
~ spl34_6,
inference(sat_conversion,[],[f5491]) ).
cnf(s234,plain,
$false,
inference(rat,[],[s5,s225,s7]) ).
fof(f5492,plain,
$false,
inference(avatar_sat_refutation,[],[s234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU176+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n018.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 03:56:24 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.49/2.38 % (2979640)Detected formulas, will run a generic FOF schedule.
% 10.49/2.38 % (2979647)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1344484712:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.49/2.38 % (2979645)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3551926698:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.49/2.38 % (2979646)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2837225363:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.49/2.38 % (2979648)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1359093704:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.49/2.38 % (2979651)dis-21_1_sil=8000:lcm=predicate:random_seed=3708061046:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.49/2.38 % (2979649)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2639460129:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.49/2.38 % (2979650)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2229340759:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.49/2.38 % (2979648)Instruction limit reached!
% 10.49/2.38 % (2979648)------------------------------
% 10.49/2.38 % (2979648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979648)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979648)Termination reason: Instruction limit
% 10.49/2.38 % (2979648)Termination phase: Saturation
% 10.49/2.38 % (2979648)Time elapsed: 0.072 s
% 10.49/2.38 % (2979648)Peak memory usage: 89 MB
% 10.49/2.38 % (2979648)Instructions burned: 110 (million)
% 10.49/2.38 % (2979649)Instruction limit reached!
% 10.49/2.38 % (2979649)------------------------------
% 10.49/2.38 % (2979649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979649)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979649)Termination reason: Instruction limit
% 10.49/2.38 % (2979649)Termination phase: Saturation
% 10.49/2.38 % (2979649)Time elapsed: 0.076 s
% 10.49/2.38 % (2979649)Peak memory usage: 89 MB
% 10.49/2.38 % (2979649)Instructions burned: 120 (million)
% 10.49/2.38 % (2979651)Instruction limit reached!
% 10.49/2.38 % (2979651)------------------------------
% 10.49/2.38 % (2979651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979651)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979651)Termination reason: Instruction limit
% 10.49/2.38 % (2979651)Termination phase: Saturation
% 10.49/2.38 % (2979651)Time elapsed: 0.080 s
% 10.49/2.38 % (2979651)Peak memory usage: 89 MB
% 10.49/2.38 % (2979651)Instructions burned: 129 (million)
% 10.49/2.38 % (2979650)Instruction limit reached!
% 10.49/2.38 % (2979650)------------------------------
% 10.49/2.38 % (2979650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979650)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979650)Termination reason: Instruction limit
% 10.49/2.38 % (2979650)Termination phase: Saturation
% 10.49/2.38 % (2979650)Time elapsed: 0.100 s
% 10.49/2.38 % (2979650)Peak memory usage: 90 MB
% 10.49/2.38 % (2979650)Instructions burned: 140 (million)
% 10.49/2.38 % (2979660)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4094250296:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.49/2.38 % (2979659)lrs+10_1_sil=8000:sp=occurrence:random_seed=2186358609:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.49/2.38 % (2979661)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2658716329:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.49/2.38 % (2979662)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1632577760:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.49/2.38 % (2979660)Instruction limit reached!
% 10.49/2.38 % (2979660)------------------------------
% 10.49/2.38 % (2979660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979660)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979660)Termination reason: Instruction limit
% 10.49/2.38 % (2979660)Termination phase: Saturation
% 10.49/2.38 % (2979660)Time elapsed: 0.085 s
% 10.49/2.38 % (2979660)Peak memory usage: 91 MB
% 10.49/2.38 % (2979660)Instructions burned: 158 (million)
% 10.49/2.38 % (2979659)Instruction limit reached!
% 10.49/2.38 % (2979659)------------------------------
% 10.49/2.38 % (2979659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979659)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979659)Termination reason: Instruction limit
% 10.49/2.38 % (2979659)Termination phase: Saturation
% 10.49/2.38 % (2979659)Time elapsed: 0.185 s
% 10.49/2.38 % (2979659)Peak memory usage: 91 MB
% 10.49/2.38 % (2979659)Instructions burned: 285 (million)
% 10.49/2.38 % (2979662)Instruction limit reached!
% 10.49/2.38 % (2979662)------------------------------
% 10.49/2.38 % (2979662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979662)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979662)Termination reason: Instruction limit
% 10.49/2.38 % (2979662)Termination phase: Saturation
% 10.49/2.38 % (2979662)Time elapsed: 0.150 s
% 10.49/2.38 % (2979662)Peak memory usage: 92 MB
% 10.49/2.38 % (2979662)Instructions burned: 248 (million)
% 10.49/2.38 % (2979667)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3886517979:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.49/2.38 % (2979661)Instruction limit reached!
% 10.49/2.38 % (2979661)------------------------------
% 10.49/2.38 % (2979661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979661)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979661)Termination reason: Instruction limit
% 10.49/2.38 % (2979661)Termination phase: Saturation
% 10.49/2.38 % (2979661)Time elapsed: 0.233 s
% 10.49/2.38 % (2979661)Peak memory usage: 92 MB
% 10.49/2.38 % (2979661)Instructions burned: 325 (million)
% 10.49/2.38 % (2979667)Instruction limit reached!
% 10.49/2.38 % (2979667)------------------------------
% 10.49/2.38 % (2979667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979667)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979667)Termination reason: Instruction limit
% 10.49/2.38 % (2979667)Termination phase: Saturation
% 10.49/2.38 % (2979667)Time elapsed: 0.103 s
% 10.49/2.38 % (2979667)Peak memory usage: 90 MB
% 10.49/2.38 % (2979667)Instructions burned: 295 (million)
% 10.49/2.38 % (2979668)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3422402218:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.49/2.38 % (2979669)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3135567421:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 10.49/2.38 % (2979671)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=652308461:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 10.49/2.38 % (2979672)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3604219410:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 10.49/2.38 % (2979669)Instruction limit reached!
% 10.49/2.38 % (2979669)------------------------------
% 10.49/2.38 % (2979669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979669)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979669)Termination reason: Instruction limit
% 10.49/2.38 % (2979669)Termination phase: Saturation
% 10.49/2.38 % (2979669)Time elapsed: 0.067 s
% 10.49/2.38 % (2979669)Peak memory usage: 89 MB
% 10.49/2.38 % (2979669)Instructions burned: 113 (million)
% 10.49/2.38 % (2979672)Instruction limit reached!
% 10.49/2.38 % (2979672)------------------------------
% 10.49/2.38 % (2979672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979672)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979672)Termination reason: Instruction limit
% 10.49/2.38 % (2979672)Termination phase: Saturation
% 10.49/2.38 % (2979672)Time elapsed: 0.037 s
% 10.49/2.38 % (2979672)Peak memory usage: 89 MB
% 10.49/2.38 % (2979672)Instructions burned: 115 (million)
% 10.49/2.38 % (2979671)Instruction limit reached!
% 10.49/2.38 % (2979671)------------------------------
% 10.49/2.38 % (2979671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979671)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979671)Termination reason: Instruction limit
% 10.49/2.38 % (2979671)Termination phase: Saturation
% 10.49/2.38 % (2979671)Time elapsed: 0.071 s
% 10.49/2.38 % (2979671)Peak memory usage: 89 MB
% 10.49/2.38 % (2979671)Instructions burned: 128 (million)
% 10.49/2.38 % (2979677)lrs+10_1_sil=8000:sp=occurrence:random_seed=3456109643:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 10.49/2.38 % (2979678)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1854744704:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 10.49/2.38 % (2979679)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2045865708:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 10.49/2.38 % (2979678)Instruction limit reached!
% 10.49/2.38 % (2979678)------------------------------
% 10.49/2.38 % (2979678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979678)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979678)Termination reason: Instruction limit
% 10.49/2.38 % (2979678)Termination phase: Saturation
% 10.49/2.38 % (2979678)Time elapsed: 0.153 s
% 10.49/2.38 % (2979678)Peak memory usage: 92 MB
% 10.49/2.38 % (2979678)Instructions burned: 438 (million)
% 10.49/2.38 % (2979683)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2629864503:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 10.49/2.38 % (2979646)First to succeed.
% 10.49/2.38 % (2979646)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2979640"
% 10.49/2.38 % (2979683)Instruction limit reached!
% 10.49/2.38 % (2979683)------------------------------
% 10.49/2.38 % (2979683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (2979683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (2979683)CaDiCaL version: 2.1.3
% 10.49/2.38 % (2979683)Termination reason: Instruction limit
% 10.49/2.38 % (2979683)Termination phase: Saturation
% 10.49/2.38 % (2979683)Time elapsed: 0.045 s
% 10.49/2.38 % (2979683)Peak memory usage: 91 MB
% 10.49/2.38 % (2979683)Instructions burned: 136 (million)
% 10.49/2.38 % (2979685)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2126498521:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 10.49/2.38 % (2979646)Refutation found. Thanks to Tanya!
% 10.49/2.38 % SZS status Theorem for theBenchmark
% 10.49/2.38 % SZS output start Proof for theBenchmark
% See solution above
% 11.26/2.47 % (2979646)------------------------------
% 11.26/2.47 % (2979646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.26/2.47 % (2979646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.26/2.47 % (2979646)CaDiCaL version: 2.1.3
% 11.26/2.47 % (2979646)Termination reason: Refutation
% 11.26/2.47 % (2979646)Time elapsed: 1.106 s
% 11.26/2.47 % (2979646)Peak memory usage: 137 MB
% 11.26/2.47 % (2979646)Instructions burned: 1657 (million)
% 11.26/2.47 % (2979646)------------------------------
% 11.26/2.47 % (2979646)------------------------------
% 11.26/2.47 % (2979640)Success in time 1.524 s
% 11.26/2.47 % Vampire exiting
%------------------------------------------------------------------------------