%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PRO012+2 : 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 : n011.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 12:30:26 PM UTC 2026
% Result : Theorem 2.68s 1.35s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 5 unt; 0 def)
% Number of atoms : 160 ( 8 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 215 ( 94 ~; 81 |; 35 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 69 ( 55 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( min_precedes(X0,X1,X3)
& min_precedes(X1,X2,X3) )
=> min_precedes(X0,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos) ).
fof(f33,axiom,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2,X3] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& occurrence_of(X2,tptp4)
& min_precedes(X1,X2,tptp0)
& ( occurrence_of(X3,tptp2)
| occurrence_of(X3,tptp1) )
& min_precedes(X2,X3,tptp0)
& ! [X4] :
( min_precedes(X1,X4,tptp0)
=> ( X4 = X2
| X4 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
fof(f46,conjecture,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& ( occurrence_of(X2,tptp2)
| occurrence_of(X2,tptp1) )
& min_precedes(X1,X2,tptp0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f47,negated_conjecture,
~ ! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& ( occurrence_of(X2,tptp2)
| occurrence_of(X2,tptp1) )
& min_precedes(X1,X2,tptp0) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f48,plain,
? [X0] :
( ! [X1,X2] :
( ~ occurrence_of(X1,tptp3)
| ~ root_occ(X1,X0)
| ( ~ occurrence_of(X2,tptp2)
& ~ occurrence_of(X2,tptp1) )
| ~ min_precedes(X1,X2,tptp0) )
& occurrence_of(X0,tptp0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ? [X1,X2,X3] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& occurrence_of(X2,tptp4)
& min_precedes(X1,X2,tptp0)
& ( occurrence_of(X3,tptp2)
| occurrence_of(X3,tptp1) )
& min_precedes(X2,X3,tptp0)
& ! [X4] :
( X4 = X2
| X4 = X3
| ~ min_precedes(X1,X4,tptp0) ) )
| ~ occurrence_of(X0,tptp0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f50,plain,
! [X0] :
( ? [X1,X2,X3] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& occurrence_of(X2,tptp4)
& min_precedes(X1,X2,tptp0)
& ( occurrence_of(X3,tptp2)
| occurrence_of(X3,tptp1) )
& min_precedes(X2,X3,tptp0)
& ! [X4] :
( X4 = X2
| X4 = X3
| ~ min_precedes(X1,X4,tptp0) ) )
| ~ occurrence_of(X0,tptp0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( min_precedes(X0,X2,X3)
| ~ min_precedes(X0,X1,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( min_precedes(X0,X2,X3)
| ~ min_precedes(X0,X1,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(flattening,[],[f51]) ).
fof(f73,plain,
( ! [X1,X2] :
( ~ occurrence_of(X1,tptp3)
| ~ root_occ(X1,sK0)
| ( ~ occurrence_of(X2,tptp2)
& ~ occurrence_of(X2,tptp1) )
| ~ min_precedes(X1,X2,tptp0) )
& occurrence_of(sK0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f48]) ).
fof(f74,plain,
! [X0] :
( ( occurrence_of(sK1(X0),tptp3)
& root_occ(sK1(X0),X0)
& occurrence_of(sK2(X0),tptp4)
& min_precedes(sK1(X0),sK2(X0),tptp0)
& ( occurrence_of(sK3(X0),tptp2)
| occurrence_of(sK3(X0),tptp1) )
& min_precedes(sK2(X0),sK3(X0),tptp0)
& ! [X4] :
( sK2(X0) = X4
| sK3(X0) = X4
| ~ min_precedes(sK1(X0),X4,tptp0) ) )
| ~ occurrence_of(X0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0)),skolemize(X3,sK3(X0))],[f50]) ).
fof(f86,plain,
occurrence_of(sK0,tptp0),
inference(cnf_transformation,[],[f73]) ).
fof(f87,plain,
! [X2,X1] :
( ~ min_precedes(X1,X2,tptp0)
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X2,tptp1)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f88,plain,
! [X2,X1] :
( ~ min_precedes(X1,X2,tptp0)
| ~ root_occ(X1,sK0)
| ~ occurrence_of(X2,tptp2)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f92,plain,
! [X0] :
( min_precedes(sK2(X0),sK3(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f93,plain,
! [X0] :
( occurrence_of(sK3(X0),tptp1)
| occurrence_of(sK3(X0),tptp2)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f94,plain,
! [X0] :
( min_precedes(sK1(X0),sK2(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f96,plain,
! [X0] :
( root_occ(sK1(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f97,plain,
! [X0] :
( occurrence_of(sK1(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( min_precedes(X0,X2,X3)
| ~ min_precedes(X0,X1,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ~ min_precedes(X1,X2,tptp0)
| ~ min_precedes(X0,X1,tptp0)
| ~ root_occ(X0,sK0)
| ~ occurrence_of(X2,tptp2)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f98,f88]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ min_precedes(X1,X2,tptp0)
| ~ min_precedes(X0,X1,tptp0)
| ~ root_occ(X0,sK0)
| ~ occurrence_of(X2,tptp1)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f98,f87]) ).
fof(f290,plain,
! [X0,X1] :
( ~ min_precedes(X0,sK2(X1),tptp0)
| ~ root_occ(X0,sK0)
| ~ occurrence_of(sK3(X1),tptp2)
| ~ occurrence_of(X0,tptp3)
| ~ occurrence_of(X1,tptp0) ),
inference(resolution,[],[f228,f92]) ).
fof(f298,plain,
! [X0,X1] :
( ~ min_precedes(X0,sK2(X1),tptp0)
| ~ root_occ(X0,sK0)
| ~ occurrence_of(sK3(X1),tptp1)
| ~ occurrence_of(X0,tptp3)
| ~ occurrence_of(X1,tptp0) ),
inference(resolution,[],[f229,f92]) ).
fof(f366,plain,
! [X0] :
( ~ root_occ(sK1(X0),sK0)
| ~ occurrence_of(sK3(X0),tptp2)
| ~ occurrence_of(sK1(X0),tptp3)
| ~ occurrence_of(X0,tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[],[f290,f94]) ).
fof(f371,plain,
! [X0] :
( ~ root_occ(sK1(X0),sK0)
| ~ occurrence_of(sK3(X0),tptp2)
| ~ occurrence_of(sK1(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(duplicate_literal_removal,[],[f366]) ).
fof(f375,plain,
! [X0] :
( ~ root_occ(sK1(X0),sK0)
| ~ occurrence_of(sK3(X0),tptp2)
| ~ occurrence_of(X0,tptp0) ),
inference(forward_subsumption_resolution,[],[f371,f97]) ).
fof(f381,plain,
( ~ occurrence_of(sK3(sK0),tptp2)
| ~ occurrence_of(sK0,tptp0)
| ~ occurrence_of(sK0,tptp0) ),
inference(resolution,[],[f375,f96]) ).
fof(f383,plain,
( ~ occurrence_of(sK3(sK0),tptp2)
| ~ occurrence_of(sK0,tptp0) ),
inference(duplicate_literal_removal,[],[f381]) ).
fof(f384,plain,
~ occurrence_of(sK3(sK0),tptp2),
inference(forward_subsumption_resolution,[],[f383,f86]) ).
fof(f398,plain,
! [X0] :
( ~ root_occ(sK1(X0),sK0)
| ~ occurrence_of(sK3(X0),tptp1)
| ~ occurrence_of(sK1(X0),tptp3)
| ~ occurrence_of(X0,tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[],[f298,f94]) ).
fof(f403,plain,
! [X0] :
( ~ root_occ(sK1(X0),sK0)
| ~ occurrence_of(sK3(X0),tptp1)
| ~ occurrence_of(sK1(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(duplicate_literal_removal,[],[f398]) ).
fof(f407,plain,
! [X0] :
( ~ root_occ(sK1(X0),sK0)
| ~ occurrence_of(sK3(X0),tptp1)
| ~ occurrence_of(X0,tptp0) ),
inference(forward_subsumption_resolution,[],[f403,f97]) ).
fof(f409,plain,
( ~ occurrence_of(sK3(sK0),tptp1)
| ~ occurrence_of(sK0,tptp0)
| ~ occurrence_of(sK0,tptp0) ),
inference(resolution,[],[f407,f96]) ).
fof(f411,plain,
( ~ occurrence_of(sK3(sK0),tptp1)
| ~ occurrence_of(sK0,tptp0) ),
inference(duplicate_literal_removal,[],[f409]) ).
fof(f412,plain,
~ occurrence_of(sK3(sK0),tptp1),
inference(forward_subsumption_resolution,[],[f411,f86]) ).
fof(f414,plain,
( occurrence_of(sK3(sK0),tptp2)
| ~ occurrence_of(sK0,tptp0) ),
inference(resolution,[],[f412,f93]) ).
fof(f415,plain,
~ occurrence_of(sK0,tptp0),
inference(forward_subsumption_resolution,[],[f414,f384]) ).
fof(f416,plain,
$false,
inference(forward_subsumption_resolution,[],[f415,f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO012+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:22:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.68/1.35 % (2817798)Detected formulas, will run a generic FOF schedule.
% 2.68/1.35 % (2817807)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=815552552:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.35 % (2817807)First to succeed.
% 2.68/1.35 % (2817807)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2817798"
% 2.68/1.35 % (2817806)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3505520527:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.35 % (2817806)Refutation not found, incomplete strategy
% 2.68/1.35 % (2817806)------------------------------
% 2.68/1.35 % (2817806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.35 % (2817806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.35 % (2817805)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=3880201472:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.35 % (2817804)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=3775247151:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.35 % (2817803)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=414752710:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.35 % (2817806)CaDiCaL version: 2.1.3
% 2.68/1.35 % (2817806)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.35 % (2817806)Time elapsed: 0.002 s
% 2.68/1.35 % (2817806)Peak memory usage: 88 MB
% 2.68/1.35 % (2817806)Instructions burned: 2 (million)
% 2.68/1.35 % (2817809)dis-21_1_sil=8000:lcm=predicate:random_seed=4117732183: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)
% 2.68/1.35 % (2817808)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3243004986:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.35 % (2817809)Also succeeded, but the first one will report.
% 2.68/1.35 % (2817808)Also succeeded, but the first one will report.
% 2.68/1.35 % (2817807)Refutation found. Thanks to Tanya!
% 2.68/1.35 % SZS status Theorem for theBenchmark
% 2.68/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.35 % (2817807)------------------------------
% 2.68/1.35 % (2817807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.35 % (2817807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.35 % (2817807)CaDiCaL version: 2.1.3
% 2.68/1.35 % (2817807)Termination reason: Refutation
% 2.68/1.35 % (2817807)Time elapsed: 0.006 s
% 2.68/1.35 % (2817807)Peak memory usage: 88 MB
% 2.68/1.35 % (2817807)Instructions burned: 15 (million)
% 2.68/1.35 % (2817807)------------------------------
% 2.68/1.35 % (2817807)------------------------------
% 2.68/1.35 % (2817798)Success in time 0.296 s
% 2.68/1.35 % Vampire exiting
%------------------------------------------------------------------------------