%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU819^2 : 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 : n012.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 08:33:49 AM UTC 2026
% Result : Theorem 0.05s 0.16s
% Output : Refutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 89 ( 42 unt; 0 typ; 3 def)
% Number of atoms : 783 ( 150 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 1308 ( 52 ~; 90 |; 51 &; 883 @)
% ( 3 <=>; 145 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 37 ( 32 usr; 11 con; 0-4 aty)
% ( 78 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 210 ( 0 sgn 78 !; 3 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
nonempty: $i > $o ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
setunionTransitive: $o ).
thf(func_def_9,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_10,type,
wellorderedByIn: $i > $o ).
thf(func_def_11,type,
ordinal: $i > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
sK1: $i > $i ).
thf(func_def_29,type,
sK3: $i > $i ).
thf(func_def_30,type,
sK4: $i > $i ).
thf(f1,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(f2,axiom,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(f3,axiom,
( setunionTransitive
= ( ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionTransitive) ).
thf(f4,axiom,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X1 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(f5,axiom,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(f6,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(f7,conjecture,
( setunionTransitive
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionOrdinalLem1) ).
thf(f8,negated_conjecture,
~ ( setunionTransitive
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f10,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( setunionTransitive
= ( ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( setunionTransitive
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( transitiveset @ Y1 ) ) )
=> ( transitiveset @ ( setunion @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( ( in @ X5 @ X6 )
& ( in @ X4 @ X5 ) )
=> ( in @ X4 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f19,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
~ ( setunionTransitive
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f21,plain,
~ ( ( setunionTransitive = $true )
=> ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ordinal @ X1 )
= $true ) )
=> ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( ? [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
!= $true )
& ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( setunionTransitive = $true ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f23,plain,
( ( $true
!= ( transitiveset @ ( setunion @ sK0 ) ) )
& ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
| ( $true
!= ( in @ X1 @ sK0 ) ) )
& ( setunionTransitive = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f22]) ).
thf(f24,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f25,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f26,plain,
( setunionTransitive
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( transitiveset @ Y1 ) ) )
=> ( transitiveset @ ( setunion @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f27,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f28,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f30,plain,
setunionTransitive = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f31,plain,
! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
| ( $true
!= ( in @ X1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
( $true
!= ( transitiveset @ ( setunion @ sK0 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f35,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y2 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 )
| ( in @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) ) )
@ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( ^ [Y2: $i] : ( emptyset != Y2 )
@ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f28,f27,f24]) ).
thf(f36,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f29,f25,f35]) ).
thf(f37,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( subset @ Y3 @ Y2 ) ) )
@ Y1 ) ) )
=> ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ ( setunion @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f26,f30,f25,f25]) ).
thf(f38,plain,
( $true
!= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ ( setunion @ sK0 ) ) ),
inference(definition_unfolding,[],[f32,f25]) ).
thf(f39,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) )
@ X1 ) )
| ( $true
!= ( in @ X1 @ sK0 ) ) ),
inference(definition_unfolding,[],[f31,f36]) ).
thf(f40,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
| ( $true
!= ( in @ X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f42,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) )
| ( $true
!= ( in @ X1 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) )
@ X2 ) )
| ( $true
!= ( in @ X1 @ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ X1 )
=> ( subset @ X2 @ X1 ) ) )
| ( $true
!= ( in @ X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f91,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
=> ( subset @ Y0 @ ( setunion @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f92,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
=> ( subset @ Y0 @ ( setunion @ sK0 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f91]) ).
thf(f93,plain,
( $false
= ( ( in @ sK2 @ ( setunion @ sK0 ) )
=> ( subset @ sK2 @ ( setunion @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
( $false
= ( subset @ sK2 @ ( setunion @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( $true
= ( in @ sK2 @ ( setunion @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f96,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( subset @ Y3 @ Y2 ) ) )
@ Y1 ) ) )
=> ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ ( setunion @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f97,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
=> ( subset @ Y0 @ ( setunion @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f98,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
=> ( subset @ Y0 @ ( setunion @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
=> ( subset @ Y0 @ ( setunion @ X1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
=> ( subset @ Y0 @ ( setunion @ X1 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK3 @ X1 ) @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( sK3 @ X1 ) )
=> ( subset @ Y0 @ ( sK3 @ X1 ) ) ) ) ) )
| ( $true
= ( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( sK3 @ X1 ) )
=> ( subset @ Y0 @ ( sK3 @ X1 ) ) ) ) )
| ( $true
= ( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X1 ) @ X1 ) )
| ( $true
= ( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f101]) ).
thf(f104,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X1 ) @ X1 ) )
| ( $true
= ( subset @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( sK3 @ X1 ) )
=> ( subset @ Y0 @ ( sK3 @ X1 ) ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f102]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( sK3 @ X1 ) )
=> ( subset @ Y0 @ ( sK3 @ X1 ) ) )
@ ( sK4 @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $true
= ( subset @ X2 @ ( setunion @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK4 @ X1 ) @ ( sK3 @ X1 ) )
=> ( subset @ ( sK4 @ X1 ) @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( $true
= ( subset @ X2 @ ( setunion @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ ( sK4 @ X1 ) @ ( sK3 @ X1 ) ) )
| ( $true
= ( subset @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 ) @ ( sK3 @ X1 ) ) )
| ( $true
= ( subset @ X2 @ ( setunion @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f112,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $false
= ( in @ X0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( subset @ X0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( subset @ X1 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f45,f104]) ).
thf(f113,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( subset @ X0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( subset @ X1 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f117,definition,
( spl5_1
<=> ! [X1: $i] :
( ( $true
= ( subset @ X1 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f118,plain,
( ! [X1: $i] :
( ( $true
= ( subset @ X1 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ sK0 ) ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f120,definition,
( spl5_2
<=> ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( subset @ X0 @ ( sK3 @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f121,plain,
( ! [X0: $i] :
( ( $true
= ( subset @ X0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( in @ X0 @ ( sK3 @ sK0 ) ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f122,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f113,f120,f117]) ).
thf(f135,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( subset @ X0 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ ( sK4 @ sK0 ) @ ( sK3 @ sK0 ) ) ) )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f108,f121]) ).
thf(f138,plain,
( ! [X0: $i] :
( ( $true
= ( subset @ X0 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ ( sK4 @ sK0 ) @ ( sK3 @ sK0 ) ) ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f135]) ).
thf(f140,definition,
( spl5_5
<=> ( $false
= ( in @ ( sK4 @ sK0 ) @ ( sK3 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f142,plain,
( ( $false
= ( in @ ( sK4 @ sK0 ) @ ( sK3 @ sK0 ) ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f140]) ).
thf(f144,plain,
( spl5_5
| spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f138,f120,f117,f140]) ).
thf(f146,plain,
( ( $true = $false )
| ( $false
= ( in @ sK2 @ ( setunion @ sK0 ) ) )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f94,f118]) ).
thf(f147,plain,
( ( $false
= ( in @ sK2 @ ( setunion @ sK0 ) ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f149,plain,
( ( $true = $false )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f147,f95]) ).
thf(f153,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f149]) ).
thf(f154,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f153]) ).
thf(f156,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( subset @ X0 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) ) )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f142,f109]) ).
thf(f157,plain,
( ! [X0: $i] :
( ( $true
= ( subset @ X0 @ ( setunion @ sK0 ) ) )
| ( $false
= ( in @ X0 @ ( setunion @ sK0 ) ) ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f159,plain,
( spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f157,f140,f117]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f122]) ).
cnf(s5,plain,
( spl5_1
| ~ spl5_2
| spl5_5 ),
inference(sat_conversion,[],[f144]) ).
cnf(s7,plain,
~ spl5_1,
inference(sat_conversion,[],[f154]) ).
cnf(s8,plain,
( spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f159]) ).
cnf(s10,plain,
~ spl5_5,
inference(rat,[],[s8,s7]) ).
cnf(s11,plain,
~ spl5_2,
inference(rat,[],[s5,s10,s7]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s11,s7]) ).
thf(f160,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU819^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 14:34:03 UTC 2026
% 0.05/0.11 % CPUTime :
% 0.05/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.05/0.13 Running first-order model finding
% 0.05/0.13 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
% 0.05/0.16 % (188824)Will run a generic schedule for satisfiability detection.
% 0.05/0.16 % (188830)% WARNING: option uhcvi not known.
% 0.05/0.16 % (188834)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1948478545:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.05/0.16 % (188832)dis+10_1_sil=32000:sp=arity:random_seed=2337424626:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.05/0.16 % (188829)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2851887772_2999 on theBenchmark for (2999ds/0Mi)
% 0.05/0.16 % (188831)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3315222774:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.05/0.16 % (188833)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2428411181:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.05/0.16 % (188830)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3773765731:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.05/0.16 % (188835)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=621202104:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.05/0.16 % (188830)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.05/0.16 % (188833)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.05/0.16 % Exception at run slice level
% 0.05/0.16 % (188830)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.05/0.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.05/0.16 % (188834) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-188824-188834"...
% 0.05/0.16 % (188832) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-188824-188832"...
% 0.05/0.16 % (188835) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-188824-188835"...
% 0.05/0.16 % (188830) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-188824-188830"...
% 0.05/0.16 % (188833) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-188824-188833"...
% 0.05/0.16 % (188835)...printing done.
% 0.05/0.16 % (188834)...printing done.
% 0.05/0.16 % (188832)...printing done.
% 0.05/0.16 % (188830)...printing done.
% 0.05/0.16 % (188833)...printing done.
% 0.05/0.16 % (188835)Refutation found. Thanks to Tanya!
% 0.05/0.16 % SZS status Theorem for theBenchmark
% 0.05/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.05/0.16 % (188835)------------------------------
% 0.05/0.16 % (188835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.16 % (188835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.16 % (188835)CaDiCaL version: 2.1.3
% 0.05/0.16 % (188835)Termination reason: Refutation
% 0.05/0.16 % (188835)Time elapsed: 0.006 s
% 0.05/0.16 % (188835)Peak memory usage: 12 MB
% 0.05/0.16 % (188835)Instructions burned: 20 (million)
% 0.05/0.16 % (188824)Success in time 0.028 s
% 0.05/0.16 % Vampire exiting
%------------------------------------------------------------------------------