%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU515_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:49:24 PM UTC 2026
% Result : Theorem 2.47s 1.22s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 210 ( 40 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 146 ( 46 ~; 49 |; 16 &)
% ( 10 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 90 ( 72 fml; 18 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 52 ( 0 sgn 44 !; 8 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK3: $o ).
tff(f1,axiom,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
<=> ( ( X2 = X0 )
| in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
tff(f2,conjecture,
( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
tff(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( setadjoinAx
<=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
<=> ( ( X0 = X2 )
| in(X2,X1) ) ) ),
inference(fool_elimination,[],[f1]) ).
tff(f5,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f6,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> ( $true = (X3) ) )
=> ( ( in(X2,X1)
=> ( $true = (X3) ) )
=> ( $true = (X3) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
tff(f7,plain,
( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
<=> ( ( X0 = X2 )
| in(X2,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
tff(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
<=> ( ( X0 = X2 )
| in(X2,X1) ) )
| ~ setadjoinAx ),
inference(ennf_transformation,[],[f7]) ).
tff(f9,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(X2,X1) )
& ( ( $true = (X3) )
| ( X0 != X2 ) ) )
& in(X2,setadjoin(X0,X1)) )
& setadjoinAx ),
inference(ennf_transformation,[],[f6]) ).
tff(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(X2,X1) )
& ( ( $true = (X3) )
| ( X0 != X2 ) ) )
& in(X2,setadjoin(X0,X1)) )
& setadjoinAx ),
inference(flattening,[],[f9]) ).
tff(f11,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( in(X2,setadjoin(X0,X1))
| ( ( X0 != X2 )
& ~ in(X2,X1) ) )
& ( ( X0 = X2 )
| in(X2,X1)
| ~ in(X2,setadjoin(X0,X1)) ) )
| ~ setadjoinAx ),
inference(nnf_transformation,[],[f8]) ).
tff(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( in(X2,setadjoin(X0,X1))
| ( ( X0 != X2 )
& ~ in(X2,X1) ) )
& ( ( X0 = X2 )
| in(X2,X1)
| ~ in(X2,setadjoin(X0,X1)) ) )
| ~ setadjoinAx ),
inference(flattening,[],[f11]) ).
tff(f13,plain,
( ( $true != sK3 )
& ( ( $true = sK3 )
| ~ in(sK2,sK1) )
& ( ( $true = sK3 )
| ( sK0 != sK2 ) )
& in(sK2,setadjoin(sK0,sK1))
& setadjoinAx ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f10]) ).
tff(f14,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| in(X2,X1)
| ~ in(X2,setadjoin(X0,X1))
| ~ setadjoinAx ),
inference(cnf_transformation,[],[f12]) ).
tff(f17,plain,
setadjoinAx,
inference(cnf_transformation,[],[f13]) ).
tff(f18,plain,
in(sK2,setadjoin(sK0,sK1)),
inference(cnf_transformation,[],[f13]) ).
tff(f19,plain,
( ( $true = sK3 )
| ( sK0 != sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
tff(f20,plain,
( ( $true = sK3 )
| ~ in(sK2,sK1) ),
inference(cnf_transformation,[],[f13]) ).
tff(f21,plain,
$true != sK3,
inference(cnf_transformation,[],[f13]) ).
tff(f26,definition,
( spl4_1
<=> ( sK0 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f28,plain,
( ( sK0 != sK2 )
| spl4_1 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f30,definition,
( spl4_2
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f33,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f19,f30,f26]) ).
tff(f35,definition,
( spl4_3
<=> in(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f37,plain,
( ~ in(sK2,sK1)
| spl4_3 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f38,plain,
( ~ spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f20,f30,f35]) ).
tff(f39,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f21,f30]) ).
tff(f41,definition,
( spl4_4
<=> setadjoinAx ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f45,definition,
( spl4_5
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ~ in(X2,setadjoin(X0,X1))
| in(X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f46,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( in(X2,X1)
| ~ in(X2,setadjoin(X0,X1))
| ( X0 = X2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f45]) ).
tff(f47,plain,
( ~ spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f14,f45,f41]) ).
tff(f56,plain,
spl4_4,
inference(avatar_split_clause,[],[f17,f41]) ).
tff(f68,plain,
( ! [X0: $i] :
( ~ in(sK2,setadjoin(X0,sK1))
| ( sK2 = X0 ) )
| spl4_3
| ~ spl4_5 ),
inference(resolution,[],[f46,f37]) ).
tff(f75,plain,
( ( sK0 = sK2 )
| spl4_3
| ~ spl4_5 ),
inference(resolution,[],[f68,f18]) ).
tff(f79,plain,
( $false
| spl4_1
| spl4_3
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f75,f28]) ).
tff(f80,plain,
( spl4_1
| spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f79]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f39]) ).
cnf(s4,plain,
( ~ spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f47]) ).
cnf(s7,plain,
spl4_4,
inference(sat_conversion,[],[f56]) ).
cnf(s8,plain,
( spl4_1
| spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f80]) ).
cnf(s11,plain,
spl4_5,
inference(rat,[],[s4,s7]) ).
cnf(s12,plain,
~ spl4_3,
inference(rat,[],[s2,s3]) ).
cnf(s13,plain,
spl4_1,
inference(rat,[],[s8,s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s3,s13]) ).
tff(f81,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU515_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 05:41:07 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
% 2.47/1.22 % (882702)Detected formulas, will run a generic FOF schedule.
% 2.47/1.22 % (882712)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2944917626:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.47/1.22 % (882712)First to succeed.
% 2.47/1.22 % (882712)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-882702"
% 2.47/1.22 % (882710)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1240233884:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.47/1.22 % (882710)Also succeeded, but the first one will report.
% 2.47/1.22 % (882709)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=615792905:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.47/1.22 % (882707)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=3149447725:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.47/1.22 % (882708)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=2242957156:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.47/1.22 % (882713)dis-21_1_sil=8000:lcm=predicate:random_seed=2788599724: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)
% 2.47/1.22 % (882713)Also succeeded, but the first one will report.
% 2.47/1.22 % (882711)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=592716250:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.47/1.22 % (882711)Also succeeded, but the first one will report.
% 2.47/1.22 % (882712)Refutation found. Thanks to Tanya!
% 2.47/1.22 % SZS status Theorem for theBenchmark
% 2.47/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/1.22 % (882712)------------------------------
% 2.47/1.22 % (882712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.22 % (882712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.22 % (882712)CaDiCaL version: 2.1.3
% 2.47/1.22 % (882712)Termination reason: Refutation
% 2.47/1.22 % (882712)Time elapsed: 0.002 s
% 2.47/1.22 % (882712)Peak memory usage: 90 MB
% 2.47/1.22 % (882712)Instructions burned: 3 (million)
% 2.47/1.22 % (882712)------------------------------
% 2.47/1.22 % (882712)------------------------------
% 2.47/1.22 % (882702)Success in time 0.273 s
% 2.47/1.22 % Vampire exiting
%------------------------------------------------------------------------------