%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU523_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 : n026.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 12:49:26 PM UTC 2026
% Result : Theorem 5.25s 1.92s
% Output : Refutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 226 ( 12 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 179 ( 72 ~; 57 |; 19 &)
% ( 10 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 88 ( 76 fml; 12 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 64 ( 0 sgn 52 !; 12 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK3: $o ).
tff(f1,axiom,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
<=> ? [X2: $i] :
( in(X1,X2)
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
tff(f2,conjecture,
( setunionAx
=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3: $i] :
( in(X1,X3)
=> ( in(X3,X0)
=> (X2) ) )
=> (X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
tff(f3,negated_conjecture,
~ ( setunionAx
=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3: $i] :
( in(X1,X3)
=> ( in(X3,X0)
=> (X2) ) )
=> (X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( setunionAx
<=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
<=> ? [X2: $i] :
( in(X1,X2)
& in(X2,X0) ) ) ),
inference(fool_elimination,[],[f1]) ).
tff(f5,plain,
~ ( setunionAx
=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3: $i] :
( in(X1,X3)
=> ( in(X3,X0)
=> (X2) ) )
=> (X2) ) ) ),
inference(rectify,[],[f3]) ).
tff(f6,plain,
~ ( setunionAx
=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3: $i] :
( in(X1,X3)
=> ( in(X3,X0)
=> ( $true = (X2) ) ) )
=> ( $true = (X2) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
tff(f7,plain,
( setunionAx
=> ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
<=> ? [X2: $i] :
( in(X1,X2)
& in(X2,X0) ) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
tff(f8,plain,
( ! [X0: $i,X1: $i] :
( in(X1,setunion(X0))
<=> ? [X2: $i] :
( in(X1,X2)
& in(X2,X0) ) )
| ~ setunionAx ),
inference(ennf_transformation,[],[f7]) ).
tff(f9,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $o] :
( ( $true != (X2) )
& ! [X3: $i] :
( ( $true = (X2) )
| ~ in(X3,X0)
| ~ in(X1,X3) ) )
& in(X1,setunion(X0)) )
& setunionAx ),
inference(ennf_transformation,[],[f6]) ).
tff(f10,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $o] :
( ( $true != (X2) )
& ! [X3: $i] :
( ( $true = (X2) )
| ~ in(X3,X0)
| ~ in(X1,X3) ) )
& in(X1,setunion(X0)) )
& setunionAx ),
inference(flattening,[],[f9]) ).
tff(f11,plain,
( ! [X0: $i,X1: $i] :
( ( in(X1,setunion(X0))
| ! [X2: $i] :
( ~ in(X1,X2)
| ~ in(X2,X0) ) )
& ( ? [X2: $i] :
( in(X1,X2)
& in(X2,X0) )
| ~ in(X1,setunion(X0)) ) )
| ~ setunionAx ),
inference(nnf_transformation,[],[f8]) ).
tff(f12,plain,
( ! [X0: $i,X1: $i] :
( ( in(X1,setunion(X0))
| ! [X2: $i] :
( ~ in(X1,X2)
| ~ in(X2,X0) ) )
& ( ? [X3: $i] :
( in(X1,X3)
& in(X3,X0) )
| ~ in(X1,setunion(X0)) ) )
| ~ setunionAx ),
inference(rectify,[],[f11]) ).
tff(f13,plain,
( ! [X0: $i,X1: $i] :
( ( in(X1,setunion(X0))
| ! [X2: $i] :
( ~ in(X1,X2)
| ~ in(X2,X0) ) )
& ( ( in(X1,sK0(X0,X1))
& in(sK0(X0,X1),X0) )
| ~ in(X1,setunion(X0)) ) )
| ~ setunionAx ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f12]) ).
tff(f14,plain,
( ( $true != sK3 )
& ! [X3: $i] :
( ( $true = sK3 )
| ~ in(X3,sK1)
| ~ in(sK2,X3) )
& in(sK2,setunion(sK1))
& setunionAx ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f10]) ).
tff(f15,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X0)
| ~ in(X1,setunion(X0))
| ~ setunionAx ),
inference(cnf_transformation,[],[f13]) ).
tff(f16,plain,
! [X0: $i,X1: $i] :
( in(X1,sK0(X0,X1))
| ~ in(X1,setunion(X0))
| ~ setunionAx ),
inference(cnf_transformation,[],[f13]) ).
tff(f18,plain,
setunionAx,
inference(cnf_transformation,[],[f14]) ).
tff(f19,plain,
in(sK2,setunion(sK1)),
inference(cnf_transformation,[],[f14]) ).
tff(f20,plain,
! [X3: $i] :
( ( $true = sK3 )
| ~ in(X3,sK1)
| ~ in(sK2,X3) ),
inference(cnf_transformation,[],[f14]) ).
tff(f21,plain,
$true != sK3,
inference(cnf_transformation,[],[f14]) ).
tff(f25,definition,
( spl4_1
<=> ! [X3: $i] :
( ~ in(X3,sK1)
| ~ in(sK2,X3) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f26,plain,
( ! [X3: $i] :
( ~ in(X3,sK1)
| ~ in(sK2,X3) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f25]) ).
tff(f28,definition,
( spl4_2
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f31,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f20,f28,f25]) ).
tff(f32,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f21,f28]) ).
tff(f34,definition,
( spl4_3
<=> setunionAx ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f38,definition,
( spl4_4
<=> ! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X0)
| ~ in(X1,setunion(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f39,plain,
( ! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X0)
| ~ in(X1,setunion(X0)) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f40,plain,
( ~ spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f15,f38,f34]) ).
tff(f42,definition,
( spl4_5
<=> ! [X0: $i,X1: $i] :
( in(X1,sK0(X0,X1))
| ~ in(X1,setunion(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f43,plain,
( ! [X0: $i,X1: $i] :
( in(X1,sK0(X0,X1))
| ~ in(X1,setunion(X0)) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f42]) ).
tff(f44,plain,
( ~ spl4_3
| spl4_5 ),
inference(avatar_split_clause,[],[f16,f42,f34]) ).
tff(f49,plain,
spl4_3,
inference(avatar_split_clause,[],[f18,f34]) ).
tff(f50,plain,
( ! [X0: $i] :
( ~ in(sK2,sK0(sK1,X0))
| ~ in(X0,setunion(sK1)) )
| ~ spl4_1
| ~ spl4_4 ),
inference(resolution,[],[f39,f26]) ).
tff(f51,plain,
( ~ in(sK2,setunion(sK1))
| ~ in(sK2,setunion(sK1))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(resolution,[],[f43,f50]) ).
tff(f52,plain,
( ~ in(sK2,setunion(sK1))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(duplicate_literal_removal,[],[f51]) ).
tff(f53,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f52,f19]) ).
tff(f54,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f53]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
( ~ spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
( ~ spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f44]) ).
cnf(s6,plain,
spl4_3,
inference(sat_conversion,[],[f49]) ).
cnf(s7,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f54]) ).
cnf(s9,plain,
spl4_5,
inference(rat,[],[s4,s6]) ).
cnf(s10,plain,
spl4_4,
inference(rat,[],[s3,s6]) ).
cnf(s11,plain,
~ spl4_1,
inference(rat,[],[s7,s9,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s2,s11]) ).
tff(f55,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU523_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n026.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 28 05:44:57 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 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
% 5.25/1.92 % (3550326)Detected formulas, will run a generic FOF schedule.
% 5.25/1.92 % (3550342)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=3126181386:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.25/1.92 % (3550346)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4199689113:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.25/1.92 % (3550346)First to succeed.
% 5.25/1.92 % (3550346)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3550326"
% 5.25/1.92 % (3550341)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=2201694378:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.25/1.92 % (3550345)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3514148451:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.25/1.92 % (3550344)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3928957358:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.25/1.92 % (3550343)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=3321642469:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.25/1.92 % (3550345)Also succeeded, but the first one will report.
% 5.25/1.92 % (3550344)Also succeeded, but the first one will report.
% 5.25/1.92 % (3550347)dis-21_1_sil=8000:lcm=predicate:random_seed=433641773: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)
% 5.25/1.92 % (3550347)Also succeeded, but the first one will report.
% 5.25/1.92 % (3550346)Refutation found. Thanks to Tanya!
% 5.25/1.92 % SZS status Theorem for theBenchmark
% 5.25/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 5.25/1.92 % (3550346)------------------------------
% 5.25/1.92 % (3550346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.92 % (3550346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.92 % (3550346)CaDiCaL version: 2.1.3
% 5.25/1.92 % (3550346)Termination reason: Refutation
% 5.25/1.92 % (3550346)Time elapsed: 0.005 s
% 5.25/1.92 % (3550346)Peak memory usage: 90 MB
% 5.25/1.92 % (3550346)Instructions burned: 2 (million)
% 5.25/1.92 % (3550346)------------------------------
% 5.25/1.92 % (3550346)------------------------------
% 5.25/1.92 % (3550326)Success in time 0.616 s
% 5.25/1.92 % Vampire exiting
%------------------------------------------------------------------------------