%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC044+1 : TPTP v9.3.1. Released v2.4.0.
% 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 01:02:10 PM UTC 2026
% Result : Theorem 2.56s 1.34s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 16 unt; 3 def)
% Number of atoms : 103 ( 33 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 100 ( 35 ~; 26 |; 25 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 18 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| ~ rearsegP(X3,X2)
| nil = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| ~ rearsegP(X3,X2)
| nil = X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& rearsegP(X3,X2)
& nil != X0
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& rearsegP(X3,X2)
& nil != X0
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f120,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f213,plain,
( nil = sK7
& sK7 = sK9
& sK6 = sK8
& rearsegP(sK9,sK8)
& nil != sK6
& ssList(sK9)
& ssList(sK8)
& ssList(sK7)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f99]) ).
fof(f218,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f262,plain,
ssList(sK8),
inference(cnf_transformation,[],[f213]) ).
fof(f264,plain,
nil != sK6,
inference(cnf_transformation,[],[f213]) ).
fof(f265,plain,
rearsegP(sK9,sK8),
inference(cnf_transformation,[],[f213]) ).
fof(f266,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f213]) ).
fof(f267,plain,
sK7 = sK9,
inference(cnf_transformation,[],[f213]) ).
fof(f268,plain,
nil = sK7,
inference(cnf_transformation,[],[f213]) ).
fof(f293,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f424,plain,
nil = sK9,
inference(definition_unfolding,[],[f268,f267]) ).
fof(f425,plain,
sK8 != sK9,
inference(definition_unfolding,[],[f264,f424,f266]) ).
fof(f440,plain,
! [X0] :
( sK9 = X0
| ~ rearsegP(sK9,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f293,f424,f424]) ).
fof(f493,definition,
! [X0,X1] :
( sQ45_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ45_eqProxy])],[equality_proxy_definition]) ).
fof(f494,plain,
~ sQ45_eqProxy(sK8,sK9),
inference(equality_proxy_replacement,[],[f425,f493]) ).
fof(f514,plain,
! [X0] :
( sQ45_eqProxy(sK9,X0)
| ~ rearsegP(sK9,X0)
| ~ ssList(X0) ),
inference(equality_proxy_replacement,[],[f440,f493]) ).
fof(f553,plain,
! [X0,X1] :
( sQ45_eqProxy(X1,X0)
| ~ sQ45_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f493]) ).
fof(f615,plain,
~ sQ45_eqProxy(sK9,sK8),
inference(resolution,[],[f553,f494]) ).
fof(f623,plain,
( ~ rearsegP(sK9,sK8)
| ~ ssList(sK8) ),
inference(resolution,[],[f615,f514]) ).
fof(f638,definition,
( spl46_11
<=> ssList(sK8) ),
introduced(definition,[new_symbols(definition,[spl46_11])],[avatar_definition]) ).
fof(f639,plain,
( ~ ssList(sK8)
| spl46_11 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f697,definition,
( spl46_26
<=> rearsegP(sK9,sK8) ),
introduced(definition,[new_symbols(definition,[spl46_26])],[avatar_definition]) ).
fof(f698,plain,
( ~ rearsegP(sK9,sK8)
| spl46_26 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f699,plain,
( ~ spl46_11
| ~ spl46_26 ),
inference(avatar_split_clause,[],[f623,f697,f638]) ).
fof(f708,plain,
( $false
| spl46_11 ),
inference(resolution,[],[f639,f262]) ).
fof(f709,plain,
spl46_11,
inference(avatar_contradiction_clause,[],[f708]) ).
fof(f710,plain,
( $false
| spl46_26 ),
inference(resolution,[],[f698,f265]) ).
fof(f711,plain,
spl46_26,
inference(avatar_contradiction_clause,[],[f710]) ).
cnf(s22,plain,
( ~ spl46_11
| ~ spl46_26 ),
inference(sat_conversion,[],[f699]) ).
cnf(s25,plain,
spl46_11,
inference(sat_conversion,[],[f709]) ).
cnf(s26,plain,
spl46_26,
inference(sat_conversion,[],[f711]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s22,s26,s25]) ).
fof(f712,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC044+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n015.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 07:38:32 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 2.56/1.34 % (2451592)Detected formulas, will run a generic FOF schedule.
% 2.56/1.34 % (2451603)dis-21_1_sil=8000:lcm=predicate:random_seed=3845150847: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)
% 2.56/1.34 % (2451603)First to succeed.
% 2.56/1.34 % (2451603)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2451592"
% 2.56/1.34 % (2451600)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1331751151:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.34 % (2451598)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=3254470915:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.34 % (2451599)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=2344290036:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.34 % (2451597)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=1895259137:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.34 % (2451602)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1262887145:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.34 % (2451600)Also succeeded, but the first one will report.
% 2.56/1.34 % (2451601)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4009459187:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.34 % (2451601)Also succeeded, but the first one will report.
% 2.56/1.34 % (2451602)Also succeeded, but the first one will report.
% 2.56/1.34 % (2451603)Refutation found. Thanks to Tanya!
% 2.56/1.34 % SZS status Theorem for theBenchmark
% 2.56/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.34 % (2451603)------------------------------
% 2.56/1.34 % (2451603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.34 % (2451603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.34 % (2451603)CaDiCaL version: 2.1.3
% 2.56/1.34 % (2451603)Termination reason: Refutation
% 2.56/1.34 % (2451603)Time elapsed: 0.004 s
% 2.56/1.34 % (2451603)Peak memory usage: 90 MB
% 2.56/1.34 % (2451603)Instructions burned: 11 (million)
% 2.56/1.34 % (2451603)------------------------------
% 2.56/1.34 % (2451603)------------------------------
% 2.56/1.34 % (2451592)Success in time 0.284 s
% 2.56/1.34 % Vampire exiting
%------------------------------------------------------------------------------