%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PRO011+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 : n019.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 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 11 unt; 6 def)
% Number of atoms : 225 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 244 ( 91 ~; 80 |; 59 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 84 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0,X1,X2] :
( ( occurrence_of(X0,X2)
& leaf_occ(X1,X0) )
=> ~ ? [X3] : min_precedes(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_21) ).
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(f45,axiom,
tptp1 != tptp2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_44) ).
fof(f46,conjecture,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( leaf_occ(X2,X0)
& ( occurrence_of(X2,tptp1)
=> ~ ? [X3] :
( occurrence_of(X3,tptp2)
& subactivity_occurrence(X3,X0)
& min_precedes(X1,X3,tptp0) ) )
& ( occurrence_of(X2,tptp2)
=> ~ ? [X4] :
( occurrence_of(X4,tptp1)
& subactivity_occurrence(X4,X0)
& 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)
& subactivity_occurrence(X3,X0)
& min_precedes(X1,X3,tptp0) ) )
& ( occurrence_of(X2,tptp2)
=> ~ ? [X4] :
( occurrence_of(X4,tptp1)
& subactivity_occurrence(X4,X0)
& min_precedes(X1,X4,tptp0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ! [X3] : ~ min_precedes(X1,X3,X2)
| ~ occurrence_of(X0,X2)
| ~ leaf_occ(X1,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ! [X3] : ~ min_precedes(X1,X3,X2)
| ~ occurrence_of(X0,X2)
| ~ leaf_occ(X1,X0) ),
inference(flattening,[],[f73]) ).
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)
& subactivity_occurrence(X3,X0)
& min_precedes(X1,X3,tptp0) )
& occurrence_of(X2,tptp1) )
| ( ? [X4] :
( occurrence_of(X4,tptp1)
& subactivity_occurrence(X4,X0)
& min_precedes(X1,X4,tptp0) )
& occurrence_of(X2,tptp2) ) )
& occurrence_of(X0,tptp0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f92,definition,
! [X0,X1,X2] :
( ( ? [X4] :
( occurrence_of(X4,tptp1)
& subactivity_occurrence(X4,X0)
& min_precedes(X1,X4,tptp0) )
& occurrence_of(X2,tptp2) )
| ~ sP0(X0,X1,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f93,plain,
? [X0] :
( ! [X1,X2] :
( ~ leaf_occ(X2,X0)
| ( ? [X3] :
( occurrence_of(X3,tptp2)
& subactivity_occurrence(X3,X0)
& min_precedes(X1,X3,tptp0) )
& occurrence_of(X2,tptp1) )
| sP0(X0,X1,X2) )
& occurrence_of(X0,tptp0) ),
inference(definition_folding,[],[f91,f92]) ).
fof(f119,plain,
! [X0] :
( ( occurrence_of(sK15(X0),tptp3)
& root_occ(sK15(X0),X0)
& occurrence_of(sK16(X0),tptp4)
& next_subocc(sK15(X0),sK16(X0),tptp0)
& ( occurrence_of(sK17(X0),tptp1)
| occurrence_of(sK17(X0),tptp2) )
& next_subocc(sK16(X0),sK17(X0),tptp0)
& leaf_occ(sK17(X0),X0) )
| ~ occurrence_of(X0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X1,sK15(X0)),skolemize(X2,sK16(X0)),skolemize(X3,sK17(X0))],[f90]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( ? [X4] :
( occurrence_of(X4,tptp1)
& subactivity_occurrence(X4,X0)
& min_precedes(X1,X4,tptp0) )
& occurrence_of(X2,tptp2) )
| ~ sP0(X0,X1,X2) ),
inference(nnf_transformation,[],[f92]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( occurrence_of(X3,tptp1)
& subactivity_occurrence(X3,X0)
& min_precedes(X1,X3,tptp0) )
& occurrence_of(X2,tptp2) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( occurrence_of(sK18(X0,X1),tptp1)
& subactivity_occurrence(sK18(X0,X1),X0)
& min_precedes(X1,sK18(X0,X1),tptp0)
& occurrence_of(X2,tptp2) )
| ~ sP0(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X3,sK18(X0,X1))],[f121]) ).
fof(f123,plain,
( ! [X1,X2] :
( ~ leaf_occ(X2,sK19)
| ( occurrence_of(sK20(X1),tptp2)
& subactivity_occurrence(sK20(X1),sK19)
& min_precedes(X1,sK20(X1),tptp0)
& occurrence_of(X2,tptp1) )
| sP0(sK19,X1,X2) )
& occurrence_of(sK19,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20]),skolemize(X0,sK19),skolemize(X3,sK20(X1))],[f93]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ~ min_precedes(X1,X3,X2)
| ~ occurrence_of(X0,X2)
| ~ leaf_occ(X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f186,plain,
! [X0] :
( leaf_occ(sK17(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f204,plain,
tptp1 != tptp2,
inference(cnf_transformation,[],[f45]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| occurrence_of(X2,tptp2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| min_precedes(X1,sK18(X0,X1),tptp0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f209,plain,
occurrence_of(sK19,tptp0),
inference(cnf_transformation,[],[f123]) ).
fof(f210,plain,
! [X2,X1] :
( sP0(sK19,X1,X2)
| occurrence_of(X2,tptp1)
| ~ leaf_occ(X2,sK19) ),
inference(cnf_transformation,[],[f123]) ).
fof(f211,plain,
! [X2,X1] :
( min_precedes(X1,sK20(X1),tptp0)
| sP0(sK19,X1,X2)
| ~ leaf_occ(X2,sK19) ),
inference(cnf_transformation,[],[f123]) ).
fof(f239,definition,
( spl21_2
<=> ! [X0] : ~ occurrence_of(X0,tptp0) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f240,plain,
( ! [X0] : ~ occurrence_of(X0,tptp0)
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f244,plain,
( $false
| ~ spl21_2 ),
inference(resolution,[],[f240,f209]) ).
fof(f245,plain,
~ spl21_2,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f257,plain,
! [X0,X1] :
( occurrence_of(X0,tptp2)
| min_precedes(X1,sK20(X1),tptp0)
| ~ leaf_occ(X0,sK19) ),
inference(resolution,[],[f205,f211]) ).
fof(f268,definition,
( spl21_5
<=> ! [X0] :
( occurrence_of(X0,tptp2)
| ~ leaf_occ(X0,sK19) ) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f269,plain,
( ! [X0] :
( ~ leaf_occ(X0,sK19)
| occurrence_of(X0,tptp2) )
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f292,definition,
( spl21_11
<=> ! [X1] : min_precedes(X1,sK20(X1),tptp0) ),
introduced(definition,[new_symbols(definition,[spl21_11])],[avatar_definition]) ).
fof(f293,plain,
( ! [X1] : min_precedes(X1,sK20(X1),tptp0)
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f294,plain,
( spl21_11
| spl21_5 ),
inference(avatar_split_clause,[],[f257,f268,f292]) ).
fof(f295,plain,
( occurrence_of(sK17(sK19),tptp2)
| ~ occurrence_of(sK19,tptp0)
| ~ spl21_5 ),
inference(resolution,[],[f269,f186]) ).
fof(f296,plain,
( occurrence_of(sK17(sK19),tptp2)
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f295,f209]) ).
fof(f333,plain,
( ! [X0] :
( ~ occurrence_of(sK17(sK19),X0)
| tptp2 = X0 )
| ~ spl21_5 ),
inference(resolution,[],[f166,f296]) ).
fof(f401,definition,
( spl21_21
<=> ! [X1] :
( occurrence_of(X1,tptp1)
| ~ leaf_occ(X1,sK19) ) ),
introduced(definition,[new_symbols(definition,[spl21_21])],[avatar_definition]) ).
fof(f402,plain,
( ! [X1] :
( ~ leaf_occ(X1,sK19)
| occurrence_of(X1,tptp1) )
| ~ spl21_21 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f458,plain,
( occurrence_of(sK17(sK19),tptp1)
| ~ occurrence_of(sK19,tptp0)
| ~ spl21_21 ),
inference(resolution,[],[f402,f186]) ).
fof(f459,plain,
( occurrence_of(sK17(sK19),tptp1)
| ~ spl21_21 ),
inference(forward_subsumption_resolution,[],[f458,f209]) ).
fof(f461,plain,
( tptp1 = tptp2
| ~ spl21_5
| ~ spl21_21 ),
inference(resolution,[],[f459,f333]) ).
fof(f467,plain,
( $false
| ~ spl21_5
| ~ spl21_21 ),
inference(forward_subsumption_resolution,[],[f461,f204]) ).
fof(f468,plain,
( ~ spl21_5
| ~ spl21_21 ),
inference(avatar_contradiction_clause,[],[f467]) ).
fof(f533,plain,
! [X0,X1] :
( min_precedes(X0,sK18(sK19,X0),tptp0)
| occurrence_of(X1,tptp1)
| ~ leaf_occ(X1,sK19) ),
inference(resolution,[],[f206,f210]) ).
fof(f572,definition,
( spl21_41
<=> ! [X0] : min_precedes(X0,sK18(sK19,X0),tptp0) ),
introduced(definition,[new_symbols(definition,[spl21_41])],[avatar_definition]) ).
fof(f573,plain,
( ! [X0] : min_precedes(X0,sK18(sK19,X0),tptp0)
| ~ spl21_41 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f574,plain,
( spl21_21
| spl21_41 ),
inference(avatar_split_clause,[],[f533,f572,f401]) ).
fof(f591,plain,
( ! [X0,X1] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,tptp0) )
| ~ spl21_41 ),
inference(resolution,[],[f573,f165]) ).
fof(f627,plain,
( ! [X0] :
( ~ occurrence_of(X0,tptp0)
| ~ occurrence_of(X0,tptp0) )
| ~ spl21_41 ),
inference(resolution,[],[f591,f186]) ).
fof(f630,plain,
( ! [X0] : ~ occurrence_of(X0,tptp0)
| ~ spl21_41 ),
inference(duplicate_literal_removal,[],[f627]) ).
fof(f631,plain,
( spl21_2
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f630,f572,f239]) ).
fof(f700,plain,
( ! [X0,X1] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,tptp0) )
| ~ spl21_11 ),
inference(resolution,[],[f293,f165]) ).
fof(f712,plain,
( ! [X0] :
( ~ occurrence_of(X0,tptp0)
| ~ occurrence_of(X0,tptp0) )
| ~ spl21_11 ),
inference(resolution,[],[f700,f186]) ).
fof(f715,plain,
( ! [X0] : ~ occurrence_of(X0,tptp0)
| ~ spl21_11 ),
inference(duplicate_literal_removal,[],[f712]) ).
fof(f716,plain,
( spl21_2
| ~ spl21_11 ),
inference(avatar_split_clause,[],[f715,f292,f239]) ).
cnf(s2,plain,
~ spl21_2,
inference(sat_conversion,[],[f245]) ).
cnf(s10,plain,
( spl21_5
| spl21_11 ),
inference(sat_conversion,[],[f294]) ).
cnf(s30,plain,
( ~ spl21_5
| ~ spl21_21 ),
inference(sat_conversion,[],[f468]) ).
cnf(s40,plain,
( spl21_21
| spl21_41 ),
inference(sat_conversion,[],[f574]) ).
cnf(s43,plain,
( spl21_2
| ~ spl21_41 ),
inference(sat_conversion,[],[f631]) ).
cnf(s49,plain,
( spl21_2
| ~ spl21_11 ),
inference(sat_conversion,[],[f716]) ).
cnf(s75,plain,
~ spl21_11,
inference(rat,[],[s49,s2]) ).
cnf(s76,plain,
~ spl21_41,
inference(rat,[],[s43,s2]) ).
cnf(s78,plain,
spl21_5,
inference(rat,[],[s10,s75]) ).
cnf(s79,plain,
spl21_21,
inference(rat,[],[s40,s76]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s30,s79,s78]) ).
fof(f717,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO011+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 22:21:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.44 % (3468117)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (3468125)dis+10_1_sil=32000:sp=arity:random_seed=2118319665:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.44 % (3468122)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1297252378_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.44 % (3468124)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=703617379:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.44 % (3468125) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3468117-3468125"...
% 0.09/0.44 % (3468128)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4239278410:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.44 % (3468126)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4282038898:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.44 % (3468127)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=682899774:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.44 % (3468123)% WARNING: option uhcvi not known.
% 0.09/0.44 % (3468125)...printing done.
% 0.09/0.44 % (3468125)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (3468125)------------------------------
% 0.09/0.44 % (3468125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (3468125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (3468125)CaDiCaL version: 2.1.3
% 0.09/0.44 % (3468125)Termination reason: Refutation
% 0.09/0.44 % (3468125)Time elapsed: 0.008 s
% 0.09/0.44 % (3468125)Peak memory usage: 13 MB
% 0.09/0.44 % (3468125)Instructions burned: 18 (million)
% 0.09/0.44 % (3468117)Success in time 0.039 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------