%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PRO010+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:30:25 PM UTC 2026
% Result : Theorem 2.67s 1.34s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 6 unt; 1 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 126 ( 34 ~; 35 |; 46 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-1 aty)
% Number of variables : 73 ( 51 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] :
( occurrence_of(X0,X1)
=> ( arboreal(X0)
<=> atomic(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(f47,axiom,
! [X0,X1,X2] :
( min_precedes(X0,X1,X2)
=> arboreal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_46) ).
fof(f50,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_49) ).
fof(f52,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_51) ).
fof(f63,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(f64,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)],[f63]) ).
fof(f65,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,[],[f64]) ).
fof(f66,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,[],[f50]) ).
fof(f95,plain,
! [X0,X1,X2] :
( arboreal(X0)
| ~ min_precedes(X0,X1,X2) ),
inference(ennf_transformation,[],[f47]) ).
fof(f102,plain,
! [X0,X1] :
( ( arboreal(X0)
<=> atomic(X1) )
| ~ occurrence_of(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f114,definition,
! [X1,X2] :
( ( ? [X4] :
( occurrence_of(X4,tptp1)
& min_precedes(X1,X4,tptp0) )
& occurrence_of(X2,tptp2) )
| ~ sP0(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f115,plain,
? [X0] :
( ! [X1,X2] :
( ~ leaf_occ(X2,X0)
| ( ? [X3] :
( occurrence_of(X3,tptp2)
& min_precedes(X1,X3,tptp0) )
& occurrence_of(X2,tptp1) )
| sP0(X1,X2) )
& occurrence_of(X0,tptp0) ),
inference(definition_folding,[],[f65,f114]) ).
fof(f116,plain,
! [X1,X2] :
( ( ? [X4] :
( occurrence_of(X4,tptp1)
& min_precedes(X1,X4,tptp0) )
& occurrence_of(X2,tptp2) )
| ~ sP0(X1,X2) ),
inference(nnf_transformation,[],[f114]) ).
fof(f117,plain,
! [X0,X1] :
( ( ? [X2] :
( occurrence_of(X2,tptp1)
& min_precedes(X0,X2,tptp0) )
& occurrence_of(X1,tptp2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( ( occurrence_of(sK1(X0),tptp1)
& min_precedes(X0,sK1(X0),tptp0)
& occurrence_of(X1,tptp2) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0))],[f117]) ).
fof(f119,plain,
( ! [X1,X2] :
( ~ leaf_occ(X2,sK2)
| ( occurrence_of(sK3(X1),tptp2)
& min_precedes(X1,sK3(X1),tptp0)
& occurrence_of(X2,tptp1) )
| sP0(X1,X2) )
& occurrence_of(sK2,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X3,sK3(X1))],[f115]) ).
fof(f120,plain,
! [X0] :
( ( occurrence_of(sK4(X0),tptp3)
& root_occ(sK4(X0),X0)
& occurrence_of(sK5(X0),tptp4)
& next_subocc(sK4(X0),sK5(X0),tptp0)
& ( occurrence_of(sK6(X0),tptp1)
| occurrence_of(sK6(X0),tptp2) )
& next_subocc(sK5(X0),sK6(X0),tptp0)
& leaf_occ(sK6(X0),X0) )
| ~ occurrence_of(X0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0)),skolemize(X3,sK6(X0))],[f66]) ).
fof(f129,plain,
! [X0,X1] :
( ( ( arboreal(X0)
| ~ atomic(X1) )
& ( atomic(X1)
| ~ arboreal(X0) ) )
| ~ occurrence_of(X0,X1) ),
inference(nnf_transformation,[],[f102]) ).
fof(f135,plain,
! [X0,X1] :
( min_precedes(X0,sK1(X0),tptp0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f137,plain,
occurrence_of(sK2,tptp0),
inference(cnf_transformation,[],[f119]) ).
fof(f139,plain,
! [X2,X1] :
( min_precedes(X1,sK3(X1),tptp0)
| ~ leaf_occ(X2,sK2)
| sP0(X1,X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f141,plain,
~ atomic(tptp0),
inference(cnf_transformation,[],[f52]) ).
fof(f143,plain,
! [X0] :
( leaf_occ(sK6(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ min_precedes(X0,X1,X2)
| arboreal(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f189,plain,
! [X0,X1] :
( ~ occurrence_of(X0,X1)
| ~ arboreal(X0)
| atomic(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f204,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ leaf_occ(X1,sK2)
| arboreal(X0) ),
inference(resolution,[],[f185,f139]) ).
fof(f207,plain,
( ~ arboreal(sK2)
| atomic(tptp0) ),
inference(resolution,[],[f189,f137]) ).
fof(f211,plain,
~ arboreal(sK2),
inference(forward_subsumption_resolution,[],[f207,f141]) ).
fof(f228,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| arboreal(X0) ),
inference(resolution,[],[f135,f185]) ).
fof(f246,plain,
! [X0,X1] :
( arboreal(X0)
| ~ leaf_occ(X1,sK2)
| arboreal(X0) ),
inference(resolution,[],[f228,f204]) ).
fof(f248,plain,
! [X0,X1] :
( ~ leaf_occ(X1,sK2)
| arboreal(X0) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f251,plain,
! [X0] :
( arboreal(X0)
| ~ occurrence_of(sK2,tptp0) ),
inference(resolution,[],[f248,f143]) ).
fof(f252,plain,
! [X0] : arboreal(X0),
inference(forward_subsumption_resolution,[],[f251,f137]) ).
fof(f253,plain,
$false,
inference(resolution,[],[f252,f211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO010+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:23:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.67/1.34 % (2074022)Detected formulas, will run a generic FOF schedule.
% 2.67/1.34 % (2074031)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3499816716:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.34 % (2074031)First to succeed.
% 2.67/1.34 % (2074031)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2074022"
% 2.67/1.34 % (2074027)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=2908523636:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.34 % (2074030)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3684477406:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.34 % (2074029)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=1998740369:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.34 % (2074032)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4247003459:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.34 % (2074033)dis-21_1_sil=8000:lcm=predicate:random_seed=2557422249: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)
% 2.67/1.34 % (2074028)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=3810954036:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.34 % (2074030)Refutation not found, incomplete strategy
% 2.67/1.34 % (2074030)------------------------------
% 2.67/1.34 % (2074030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.34 % (2074030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.34 % (2074030)CaDiCaL version: 2.1.3
% 2.67/1.34 % (2074030)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.34 % (2074030)Time elapsed: 0.002 s
% 2.67/1.34 % (2074030)Peak memory usage: 88 MB
% 2.67/1.34 % (2074030)Instructions burned: 1 (million)
% 2.67/1.34 % (2074033)Also succeeded, but the first one will report.
% 2.67/1.34 % (2074032)Instruction limit reached!
% 2.67/1.34 % (2074032)------------------------------
% 2.67/1.34 % (2074032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.34 % (2074032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.34 % (2074032)CaDiCaL version: 2.1.3
% 2.67/1.34 % (2074032)Termination reason: Instruction limit
% 2.67/1.34 % (2074032)Termination phase: Saturation
% 2.67/1.34 % (2074032)Time elapsed: 0.098 s
% 2.67/1.34 % (2074032)Peak memory usage: 90 MB
% 2.67/1.34 % (2074032)Instructions burned: 139 (million)
% 2.67/1.34 % (2074031)Refutation found. Thanks to Tanya!
% 2.67/1.34 % SZS status Theorem for theBenchmark
% 2.67/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.34 % (2074031)------------------------------
% 2.67/1.34 % (2074031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.34 % (2074031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.34 % (2074031)CaDiCaL version: 2.1.3
% 2.67/1.34 % (2074031)Termination reason: Refutation
% 2.67/1.34 % (2074031)Time elapsed: 0.002 s
% 2.67/1.34 % (2074031)Peak memory usage: 88 MB
% 2.67/1.34 % (2074031)Instructions burned: 4 (million)
% 2.67/1.34 % (2074031)------------------------------
% 2.67/1.34 % (2074031)------------------------------
% 2.67/1.34 % (2074022)Success in time 0.29 s
% 2.67/1.34 % Vampire exiting
%------------------------------------------------------------------------------