%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU530^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 : Wed Sep 30 08:32:19 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 30 unt; 0 typ; 1 def)
% Number of atoms : 254 ( 73 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 263 ( 13 ~; 6 |; 9 &; 188 @)
% ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 9 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 60 ( 0 sgn 36 !; 4 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
uniqinunit: $o ).
thf(func_def_5,type,
eqinunit: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(f1,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(f2,axiom,
( eqinunit
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(f3,conjecture,
( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(f4,negated_conjecture,
~ ( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( eqinunit
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( uniqinunit = $true )
=> ( ( eqinunit = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) )
& ( eqinunit = $true )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) )
& ( eqinunit = $true )
& ( uniqinunit = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( $true
!= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( $true
= ( in @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) )
& ( eqinunit = $true )
& ( uniqinunit = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
eqinunit = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
= ( in @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
!= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f17]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( X2 = X1 )
=> ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2 = X1 ) )
| ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( ( $true != $true )
| ( sK0 != sK1 ) ),
inference(constrained_superposition,[],[f19,f29]) ).
thf(f37,plain,
sK0 != sK1,
inference(trivial_inequality_removal,[],[f36]) ).
thf(f40,plain,
( ( $true = $false )
| ( sK0 = sK1 ) ),
inference(constrained_superposition,[],[f18,f35]) ).
thf(f43,plain,
sK0 = sK1,
inference(trivial_inequality_removal,[],[f40]) ).
thf(f46,definition,
( spl2_1
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f54,plain,
spl2_1,
inference(avatar_split_clause,[],[f43,f46]) ).
thf(f55,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f37,f46]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f54]) ).
cnf(s4,plain,
~ spl2_1,
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4]) ).
thf(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU530^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:48:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.26 % (1313463)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (1313471)dis+10_1_sil=32000:sp=arity:random_seed=1107501226:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.26 % (1313471) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1313463-1313471"...
% 0.18/0.26 % (1313469)% WARNING: option uhcvi not known.
% 0.18/0.26 % (1313471)...printing done.
% 0.18/0.26 % (1313471)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (1313471)------------------------------
% 0.18/0.26 % (1313471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (1313471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (1313471)CaDiCaL version: 2.1.3
% 0.18/0.26 % (1313471)Termination reason: Refutation
% 0.18/0.26 % (1313471)Time elapsed: 0.002 s
% 0.18/0.26 % (1313471)Peak memory usage: 12 MB
% 0.18/0.26 % (1313471)Instructions burned: 4 (million)
% 0.18/0.26 % (1313463)Success in time 0.037 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------