%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n010.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 12:53:36 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 182 ( 12 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 127 ( 46 ~; 34 |; 19 &)
% ( 7 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 82 ( 70 fml; 12 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 59 ( 0 sgn 47 !; 12 ?; 59 :)
% 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(f33,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,setunion(X0))
| in(sK0(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f15,f18]) ).
tff(f34,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,setunion(X0))
| in(X1,sK0(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f16,f18]) ).
tff(f36,plain,
in(sK0(sK1,sK2),sK1),
inference(resolution,[],[f33,f19]) ).
tff(f37,plain,
in(sK2,sK0(sK1,sK2)),
inference(resolution,[],[f34,f19]) ).
tff(f38,plain,
( ~ in(sK2,sK0(sK1,sK2))
| ~ spl4_1 ),
inference(resolution,[],[f36,f26]) ).
tff(f39,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f38,f37]) ).
tff(f40,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f39]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f41,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU523_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 05:42:32 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 % (1631360)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (1631370)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1562649181:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.45 % (1631370) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1631360-1631370"...
% 0.13/0.45 % (1631370)...printing done.
% 0.13/0.45 % (1631366)% WARNING: option uhcvi not known.
% 0.13/0.45 % (1631370)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.45 % (1631370)------------------------------
% 0.13/0.45 % (1631370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (1631370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (1631370)CaDiCaL version: 2.1.3
% 0.13/0.45 % (1631370)Termination reason: Refutation
% 0.13/0.45 % (1631370)Time elapsed: 0.001 s
% 0.13/0.45 % (1631370)Peak memory usage: 12 MB
% 0.13/0.45 % (1631370)Instructions burned: 1 (million)
% 0.13/0.45 % (1631360)Success in time 0.027 s
% 0.13/0.45 % Vampire exiting
%------------------------------------------------------------------------------