%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU531_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 : n018.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 12:49:29 PM UTC 2026
% Result : Theorem 3.51s 1.43s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 23 unt; 0 typ; 7 def)
% Number of atoms : 270 ( 43 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 170 ( 61 ~; 53 |; 16 &)
% ( 9 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 128 ( 102 fml; 26 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 15 usr; 13 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 75 ( 0 sgn 69 !; 6 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_4,type,
sQ3_eqProxy: ( $o * $o ) > $o ).
tff(f1,axiom,
( setadjoinE
= ( ! [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(f2,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( in(X0,setadjoin(X1,emptyset))
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
tff(f3,conjecture,
( setadjoinE
=> ( uniqinunit
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,setadjoin(X1,emptyset)))
=> ( ( X2 = X0 )
| ( X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
tff(f4,negated_conjecture,
~ ( setadjoinE
=> ( uniqinunit
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,setadjoin(X1,emptyset)))
=> ( ( X2 = X0 )
| ( X2 = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
( setadjoinE
= ( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ) ),
inference(rectify,[],[f1]) ).
tff(f6,plain,
( setadjoinE
<=> ! [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,
( uniqinunit
<=> ! [X0: $i,X1: $i] :
( in(X0,setadjoin(X1,emptyset))
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f2]) ).
tff(f8,plain,
( uniqinunit
=> ! [X0: $i,X1: $i] :
( in(X0,setadjoin(X1,emptyset))
=> ( X0 = X1 ) ) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
tff(f9,plain,
( setadjoinE
=> ! [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(unused_predicate_definition_removal,[],[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)) )
| ~ setadjoinE ),
inference(ennf_transformation,[],[f9]) ).
tff(f11,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)) )
| ~ setadjoinE ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,setadjoin(X1,emptyset)) )
| ~ uniqinunit ),
inference(ennf_transformation,[],[f8]) ).
tff(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X2 )
& ( X1 != X2 )
& in(X2,setadjoin(X0,setadjoin(X1,emptyset))) )
& uniqinunit
& setadjoinE ),
inference(ennf_transformation,[],[f4]) ).
tff(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X2 )
& ( X1 != X2 )
& in(X2,setadjoin(X0,setadjoin(X1,emptyset))) )
& uniqinunit
& setadjoinE ),
inference(flattening,[],[f13]) ).
tff(f15,plain,
( ( sK0 != sK2 )
& ( sK1 != sK2 )
& in(sK2,setadjoin(sK0,setadjoin(sK1,emptyset)))
& uniqinunit
& setadjoinE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14]) ).
tff(f16,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true = (X3) )
| in(X2,X1)
| ( X0 = X2 )
| ~ in(X2,setadjoin(X0,X1))
| ~ setadjoinE ),
inference(cnf_transformation,[],[f11]) ).
tff(f20,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,setadjoin(X1,emptyset))
| ~ uniqinunit ),
inference(cnf_transformation,[],[f12]) ).
tff(f21,plain,
setadjoinE,
inference(cnf_transformation,[],[f15]) ).
tff(f22,plain,
uniqinunit,
inference(cnf_transformation,[],[f15]) ).
tff(f23,plain,
in(sK2,setadjoin(sK0,setadjoin(sK1,emptyset))),
inference(cnf_transformation,[],[f15]) ).
tff(f24,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f15]) ).
tff(f25,plain,
sK0 != sK2,
inference(cnf_transformation,[],[f15]) ).
tff(f26,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f31,definition,
! [X0: $o,X1: $o] :
( sQ3_eqProxy((X0),(X1))
<=> ( (X0) = (X1) ) ),
introduced(definition,[new_symbols(definition,[sQ3_eqProxy])],[equality_proxy_definition]) ).
tff(f33,plain,
~ sQ3_eqProxy($true,$false),
inference(equality_proxy_replacement,[],[f26,f31]) ).
tff(f35,definition,
! [X0: $i,X1: $i] :
( sQ4_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
tff(f38,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( sQ3_eqProxy($true,(X3))
| in(X2,X1)
| sQ4_eqProxy(X0,X2)
| ~ in(X2,setadjoin(X0,X1))
| ~ setadjoinE ),
inference(equality_proxy_replacement,[],[f16,f31,f35]) ).
tff(f39,plain,
! [X0: $i,X1: $i] :
( sQ4_eqProxy(X0,X1)
| ~ in(X0,setadjoin(X1,emptyset))
| ~ uniqinunit ),
inference(equality_proxy_replacement,[],[f20,f35]) ).
tff(f40,plain,
~ sQ4_eqProxy(sK0,sK2),
inference(equality_proxy_replacement,[],[f25,f35]) ).
tff(f41,plain,
~ sQ4_eqProxy(sK1,sK2),
inference(equality_proxy_replacement,[],[f24,f35]) ).
tff(f43,plain,
! [X0: $i,X1: $i] :
( sQ4_eqProxy(X1,X0)
| ~ sQ4_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f35]) ).
tff(f47,definition,
( spl5_1
<=> uniqinunit ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f48,plain,
( ~ uniqinunit
| spl5_1 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f50,definition,
( spl5_2
<=> ! [X0: $i,X1: $i] :
( sQ4_eqProxy(X0,X1)
| ~ in(X0,setadjoin(X1,emptyset)) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f51,plain,
( ! [X0: $i,X1: $i] :
( sQ4_eqProxy(X0,X1)
| ~ in(X0,setadjoin(X1,emptyset)) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f50]) ).
tff(f52,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f39,f50,f47]) ).
tff(f54,definition,
( spl5_3
<=> setadjoinE ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f55,plain,
( ~ setadjoinE
| spl5_3 ),
inference(avatar_component_clause,[],[f54]) ).
tff(f57,definition,
( spl5_4
<=> ! [X2: $i,X0: $i,X1: $i] :
( in(X2,X1)
| ~ in(X2,setadjoin(X0,X1))
| sQ4_eqProxy(X0,X2) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f58,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( sQ4_eqProxy(X0,X2)
| ~ in(X2,setadjoin(X0,X1))
| in(X2,X1) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f57]) ).
tff(f60,definition,
( spl5_5
<=> ! [X3: $o] : sQ3_eqProxy($true,(X3)) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f61,plain,
( ! [X3: $o] : sQ3_eqProxy($true,(X3))
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f60]) ).
tff(f62,plain,
( ~ spl5_3
| spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f38,f60,f57,f54]) ).
tff(f74,plain,
( $false
| spl5_3 ),
inference(resolution,[],[f55,f21]) ).
tff(f75,plain,
spl5_3,
inference(avatar_contradiction_clause,[],[f74]) ).
tff(f76,plain,
( $false
| spl5_1 ),
inference(resolution,[],[f22,f48]) ).
tff(f77,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f76]) ).
tff(f79,plain,
( ! [X0: $i] :
( ~ in(sK2,setadjoin(sK0,X0))
| in(sK2,X0) )
| ~ spl5_4 ),
inference(resolution,[],[f40,f58]) ).
tff(f82,plain,
( in(sK2,setadjoin(sK1,emptyset))
| ~ spl5_4 ),
inference(resolution,[],[f23,f79]) ).
tff(f86,plain,
~ sQ4_eqProxy(sK2,sK1),
inference(resolution,[],[f43,f41]) ).
tff(f92,plain,
( ~ in(sK2,setadjoin(sK1,emptyset))
| ~ spl5_2 ),
inference(resolution,[],[f86,f51]) ).
tff(f94,plain,
( $false
| ~ spl5_2
| ~ spl5_4 ),
inference(resolution,[],[f92,f82]) ).
tff(f95,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f94]) ).
tff(f96,plain,
( $false
| ~ spl5_5 ),
inference(resolution,[],[f61,f33]) ).
tff(f97,plain,
~ spl5_5,
inference(avatar_contradiction_clause,[],[f96]) ).
cnf(s1,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s2,plain,
( ~ spl5_3
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f62]) ).
cnf(s5,plain,
spl5_3,
inference(sat_conversion,[],[f75]) ).
cnf(s6,plain,
spl5_1,
inference(sat_conversion,[],[f77]) ).
cnf(s7,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(sat_conversion,[],[f95]) ).
cnf(s8,plain,
~ spl5_5,
inference(sat_conversion,[],[f97]) ).
cnf(s11,plain,
spl5_4,
inference(rat,[],[s2,s8,s5]) ).
cnf(s12,plain,
~ spl5_2,
inference(rat,[],[s7,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s12,s6]) ).
tff(f98,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU531_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.35 % Computer : n018.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8046.5625MB
% 0.12/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Sep 28 05:44:40 UTC 2026
% 0.16/0.36 % CPUTime :
% 0.16/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.39 Running first-order theorem proving
% 0.16/0.39 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
% 3.51/1.43 % (3083820)Detected formulas, will run a generic FOF schedule.
% 3.51/1.43 % (3083829)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=24876420:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.51/1.43 % (3083829)Refutation not found, incomplete strategy
% 3.51/1.43 % (3083829)------------------------------
% 3.51/1.43 % (3083829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.43 % (3083829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.43 % (3083829)CaDiCaL version: 2.1.3
% 3.51/1.43 % (3083829)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.43 % (3083829)Time elapsed: 0.001 s
% 3.51/1.43 % (3083829)Peak memory usage: 88 MB
% 3.51/1.43 % (3083831)dis-21_1_sil=8000:lcm=predicate:random_seed=4220042950: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)
% 3.51/1.43 % (3083831)First to succeed.
% 3.51/1.43 % (3083828)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3182420380:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.51/1.43 % (3083825)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=1111477532:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.51/1.43 % (3083827)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=2725437660:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.51/1.43 % (3083826)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=3306914998:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.51/1.43 % (3083831)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3083820"
% 3.51/1.43 % (3083828)Refutation not found, incomplete strategy
% 3.51/1.43 % (3083828)------------------------------
% 3.51/1.43 % (3083828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.43 % (3083828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.43 % (3083828)CaDiCaL version: 2.1.3
% 3.51/1.43 % (3083828)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.43 % (3083828)Time elapsed: 0.001 s
% 3.51/1.43 % (3083828)Peak memory usage: 88 MB
% 3.51/1.43 % (3083830)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1994439888:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.51/1.43 % (3083830)Also succeeded, but the first one will report.
% 3.51/1.43 % (3083829)------------------------------
% 3.51/1.43 % (3083829)------------------------------
% 3.51/1.43 % (3083839)lrs+10_1_sil=8000:sp=occurrence:random_seed=1107957233:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.51/1.43 % (3083839)Also succeeded, but the first one will report.
% 3.51/1.43 % (3083828)------------------------------
% 3.51/1.43 % (3083828)------------------------------
% 3.51/1.43 % (3083831)Refutation found. Thanks to Tanya!
% 3.51/1.43 % SZS status Theorem for theBenchmark
% 3.51/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.43 % (3083831)------------------------------
% 3.51/1.43 % (3083831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.43 % (3083831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.43 % (3083831)CaDiCaL version: 2.1.3
% 3.51/1.43 % (3083831)Termination reason: Refutation
% 3.51/1.43 % (3083831)Time elapsed: 0.003 s
% 3.51/1.43 % (3083831)Peak memory usage: 89 MB
% 3.51/1.43 % (3083831)Instructions burned: 2 (million)
% 3.51/1.43 % (3083831)------------------------------
% 3.51/1.43 % (3083831)------------------------------
% 3.51/1.43 % (3083820)Success in time 0.408 s
% 3.51/1.43 % Vampire exiting
%------------------------------------------------------------------------------