%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PRO010+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:30:37 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 9 unt; 3 def)
% Number of atoms : 136 ( 7 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 138 ( 51 ~; 43 |; 30 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 4 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 46 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1] :
( leaf_occ(X0,X1)
<=> ? [X2] :
( occurrence_of(X1,X2)
& subactivity_occurrence(X0,X1)
& leaf(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
fof(f15,axiom,
! [X0,X1] :
( leaf(X0,X1)
<=> ( ( root(X0,X1)
| ? [X2] : min_precedes(X2,X0,X1) )
& ~ ? [X3] : min_precedes(X0,X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_14) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( occurrence_of(X0,X1)
& occurrence_of(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_22) ).
fof(f33,axiom,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2,X3] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& occurrence_of(X2,tptp4)
& next_subocc(X1,X2,tptp0)
& ( occurrence_of(X3,tptp1)
| occurrence_of(X3,tptp2) )
& next_subocc(X2,X3,tptp0)
& leaf_occ(X3,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
fof(f46,conjecture,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( leaf_occ(X2,X0)
& ( occurrence_of(X2,tptp1)
=> ~ ? [X3] :
( occurrence_of(X3,tptp2)
& min_precedes(X1,X3,tptp0) ) )
& ( occurrence_of(X2,tptp2)
=> ~ ? [X4] :
( occurrence_of(X4,tptp1)
& min_precedes(X1,X4,tptp0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f47,negated_conjecture,
~ ! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( leaf_occ(X2,X0)
& ( occurrence_of(X2,tptp1)
=> ~ ? [X3] :
( occurrence_of(X3,tptp2)
& min_precedes(X1,X3,tptp0) ) )
& ( occurrence_of(X2,tptp2)
=> ~ ? [X4] :
( occurrence_of(X4,tptp1)
& min_precedes(X1,X4,tptp0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f65,plain,
! [X0,X1] :
( leaf(X0,X1)
<=> ( ( root(X0,X1)
| ? [X2] : min_precedes(X2,X0,X1) )
& ! [X3] : ~ min_precedes(X0,X3,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f75,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X1)
| ~ occurrence_of(X0,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f76,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X1)
| ~ occurrence_of(X0,X2) ),
inference(flattening,[],[f75]) ).
fof(f90,plain,
! [X0] :
( ? [X1,X2,X3] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& occurrence_of(X2,tptp4)
& next_subocc(X1,X2,tptp0)
& ( occurrence_of(X3,tptp1)
| occurrence_of(X3,tptp2) )
& next_subocc(X2,X3,tptp0)
& leaf_occ(X3,X0) )
| ~ occurrence_of(X0,tptp0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f91,plain,
? [X0] :
( ! [X1,X2] :
( ~ leaf_occ(X2,X0)
| ( ? [X3] :
( occurrence_of(X3,tptp2)
& min_precedes(X1,X3,tptp0) )
& occurrence_of(X2,tptp1) )
| ( ? [X4] :
( occurrence_of(X4,tptp1)
& min_precedes(X1,X4,tptp0) )
& occurrence_of(X2,tptp2) ) )
& occurrence_of(X0,tptp0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f111,plain,
! [X0,X1] :
( leaf(X0,sK2(X0,X1))
| ~ leaf_occ(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f113,plain,
! [X0,X1] :
( ~ leaf_occ(X0,X1)
| occurrence_of(X1,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f121,plain,
! [X3,X0,X1] :
( ~ leaf(X0,X1)
| ~ min_precedes(X0,X3,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f155,plain,
! [X0] :
( leaf_occ(sK16(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f177,plain,
! [X2,X1] :
( min_precedes(X1,sK18(X1),tptp0)
| min_precedes(X1,sK19(X1),tptp0)
| ~ leaf_occ(X2,sK17) ),
inference(cnf_transformation,[],[f91]) ).
fof(f182,plain,
occurrence_of(sK17,tptp0),
inference(cnf_transformation,[],[f91]) ).
fof(f195,definition,
( spl20_4
<=> ! [X2] : ~ leaf_occ(X2,sK17) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
fof(f196,plain,
( ! [X2] : ~ leaf_occ(X2,sK17)
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f206,definition,
( spl20_7
<=> ! [X1] :
( min_precedes(X1,sK18(X1),tptp0)
| min_precedes(X1,sK19(X1),tptp0) ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
fof(f207,plain,
( ! [X1] :
( min_precedes(X1,sK19(X1),tptp0)
| min_precedes(X1,sK18(X1),tptp0) )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f208,plain,
( spl20_4
| spl20_7 ),
inference(avatar_split_clause,[],[f177,f206,f195]) ).
fof(f241,plain,
( ~ occurrence_of(sK17,tptp0)
| ~ spl20_4 ),
inference(resolution,[],[f155,f196]) ).
fof(f242,plain,
( $false
| ~ spl20_4 ),
inference(forward_subsumption_resolution,[],[f241,f182]) ).
fof(f243,plain,
~ spl20_4,
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f255,plain,
! [X2,X0,X1] :
( ~ leaf_occ(X0,X1)
| ~ min_precedes(X0,X2,sK2(X0,X1)) ),
inference(resolution,[],[f111,f121]) ).
fof(f258,plain,
! [X0] :
( occurrence_of(X0,sK2(sK16(X0),X0))
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[],[f113,f155]) ).
fof(f289,plain,
! [X0] :
( ~ occurrence_of(sK17,X0)
| tptp0 = X0 ),
inference(resolution,[],[f134,f182]) ).
fof(f606,plain,
( ~ occurrence_of(sK17,tptp0)
| tptp0 = sK2(sK16(sK17),sK17) ),
inference(resolution,[],[f258,f289]) ).
fof(f610,plain,
tptp0 = sK2(sK16(sK17),sK17),
inference(forward_subsumption_resolution,[],[f606,f182]) ).
fof(f615,definition,
( spl20_28
<=> leaf_occ(sK16(sK17),sK17) ),
introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition]) ).
fof(f616,plain,
( leaf_occ(sK16(sK17),sK17)
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f617,plain,
( ~ leaf_occ(sK16(sK17),sK17)
| spl20_28 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f628,plain,
( ~ occurrence_of(sK17,tptp0)
| spl20_28 ),
inference(resolution,[],[f617,f155]) ).
fof(f629,plain,
( $false
| spl20_28 ),
inference(forward_subsumption_resolution,[],[f628,f182]) ).
fof(f630,plain,
spl20_28,
inference(avatar_contradiction_clause,[],[f629]) ).
fof(f634,plain,
( ! [X0] : ~ min_precedes(sK16(sK17),X0,sK2(sK16(sK17),sK17))
| ~ spl20_28 ),
inference(resolution,[],[f616,f255]) ).
fof(f642,plain,
( ! [X0] : ~ min_precedes(sK16(sK17),X0,tptp0)
| ~ spl20_28 ),
inference(forward_demodulation,[],[f634,f610]) ).
fof(f672,plain,
( min_precedes(sK16(sK17),sK18(sK16(sK17)),tptp0)
| ~ spl20_7
| ~ spl20_28 ),
inference(resolution,[],[f642,f207]) ).
fof(f690,plain,
( $false
| ~ spl20_7
| ~ spl20_28 ),
inference(forward_subsumption_resolution,[],[f672,f642]) ).
fof(f691,plain,
( ~ spl20_7
| ~ spl20_28 ),
inference(avatar_contradiction_clause,[],[f690]) ).
cnf(s5,plain,
( spl20_4
| spl20_7 ),
inference(sat_conversion,[],[f208]) ).
cnf(s9,plain,
~ spl20_4,
inference(sat_conversion,[],[f243]) ).
cnf(s24,plain,
spl20_28,
inference(sat_conversion,[],[f630]) ).
cnf(s32,plain,
( ~ spl20_7
| ~ spl20_28 ),
inference(sat_conversion,[],[f691]) ).
cnf(s37,plain,
~ spl20_7,
inference(rat,[],[s32,s24]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s5,s37,s9]) ).
fof(f701,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:19:45 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 % (2465421)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2465430)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2026652602:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2465427)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2465431)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3077075164:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2465426)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3778523301_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2465427)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=634341176:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2465428)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4236723874:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2465429)dis+10_1_sil=32000:sp=arity:random_seed=3000667421:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2465432)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=706183220:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (2465430) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2465421-2465430"...
% 0.17/0.47 % (2465430)...printing done.
% 0.17/0.47 % (2465430)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (2465430)------------------------------
% 0.17/0.48 % (2465430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2465430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2465430)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2465430)Termination reason: Refutation
% 0.17/0.48 % (2465430)Time elapsed: 0.010 s
% 0.17/0.48 % (2465430)Peak memory usage: 13 MB
% 0.17/0.48 % (2465430)Instructions burned: 23 (million)
% 0.17/0.48 % (2465421)Success in time 0.047 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------