%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU802^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:20 AM UTC 2026
% Result : Theorem 1.53s 1.29s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 472 ( 107 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 647 ( 12 ~; 15 |; 28 &; 511 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 15 usr; 9 con; 0-4 aty)
% ( 28 !!; 16 ??; 0 @@+; 0 @@-)
% Number of variables : 154 ( 98 ^; 48 !; 8 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
funcSet: $i > $i > $i ).
thf(func_def_5,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_6,type,
surjective: $i > $i > $i > $o ).
thf(func_def_7,type,
surjFuncSet: $i > $i > $i ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_27,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
sK6: $i > $i ).
thf(func_def_29,type,
sK7: $i > $i ).
thf(f85,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f32,f75]) ).
thf(f75,plain,
( $false
= ( in @ sK4 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $false = $true )
| ( $false
= ( in @ sK4 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f72,f55]) ).
thf(f55,plain,
! [X1: $i] :
( ( ( in @ ( sK6 @ X1 ) @ sK2 )
= $true )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ( ( ap @ sK2 @ sK0 @ sK1 @ ( sK6 @ X1 ) )
= X1 )
& ( in @ ( sK6 @ X1 ) @ sK2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y0 )
= X1 )
& ( in @ Y0 @ sK2 ) )
@ ( sK6 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y0 )
= X1 )
& ( in @ Y0 @ sK2 ) ) ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y0 )
= X1 )
& ( in @ Y0 @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y1 )
= Y0 )
& ( in @ Y1 @ sK2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y1 )
= Y0 )
& ( in @ Y1 @ sK2 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( ap @ sK2 @ sK0 @ Y0 @ Y2 )
= Y1 )
& ( in @ Y2 @ sK2 ) ) ) ) )
@ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $false = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( ap @ sK2 @ sK0 @ Y0 @ Y2 )
= Y1 )
& ( in @ Y2 @ sK2 ) ) ) ) )
@ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f37,f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
| ( ( X3 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
=> ( X3 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( Y2 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f19]) ).
thf(f19,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i > $o,X2: $i,X0: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2THF_26111.p',dsetconstrER) ).
thf(f21,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( in @ sK1 @ ( surjFuncSet @ sK2 @ sK0 ) )
= $true )
& ( $true
!= ( surjective @ sK2 @ sK0 @ sK1 ) )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( surjFuncSet @ X2 @ X0 ) ) )
& ( $true
!= ( surjective @ X2 @ X0 @ X1 ) ) )
=> ( ( ( in @ sK1 @ ( surjFuncSet @ sK2 @ sK0 ) )
= $true )
& ( $true
!= ( surjective @ sK2 @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( surjFuncSet @ X2 @ X0 ) ) )
& ( $true
!= ( surjective @ X2 @ X0 @ X1 ) ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( surjFuncSet @ X2 @ X0 ) ) )
=> ( $true
= ( surjective @ X2 @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( surjFuncSet @ X2 @ X0 ) )
=> ( surjective @ X2 @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( dsetconstrER
=> ! [X3: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( surjFuncSet @ X2 @ X3 ) )
=> ( surjective @ X2 @ X3 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( dsetconstrER
=> ! [X3: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( surjFuncSet @ X2 @ X3 ) )
=> ( surjective @ X2 @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2THF_26111.p',surjFuncSetFuncSurj) ).
thf(f37,plain,
( ( in @ sK1
@ ( dsetconstr @ ( funcSet @ sK2 @ sK0 )
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( ap @ sK2 @ sK0 @ Y0 @ Y2 )
= Y1 )
& ( in @ Y2 @ sK2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y4 )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( ( ap @ Y3 @ Y4 @ Y5 @ Y7 )
= Y6 )
& ( in @ Y7 @ Y3 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK2
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f24]) ).
thf(f24,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y4 )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( ( ap @ Y3 @ Y4 @ Y5 @ Y7 )
= Y6 )
& ( in @ Y7 @ Y3 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f18]) ).
thf(f18,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 )
& ( in @ Y4 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 )
& ( in @ Y4 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X4: $i] :
( ( in @ X4 @ X0 )
& ( ( ap @ X0 @ X1 @ X2 @ X4 )
= X3 ) ) ) )
= surjective ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i,X4: $i,X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X3: $i] :
( ( in @ X3 @ X0 )
& ( ( ap @ X0 @ X4 @ X5 @ X3 )
= X2 ) ) ) )
= surjective ),
file('/export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2THF_26111.p',surjective) ).
thf(f20,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( surjective @ X0 @ X1 @ X2 ) ) )
= surjFuncSet ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( funcSet @ X0 @ X4 )
@ ^ [X5: $i] : ( surjective @ X0 @ X4 @ X5 ) ) )
= surjFuncSet ),
file('/export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2THF_26111.p',surjFuncSet) ).
thf(f23,plain,
( ( in @ sK1 @ ( surjFuncSet @ sK2 @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f72,plain,
( $false
= ( in @ ( sK6 @ sK4 ) @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $false
= ( in @ ( sK6 @ sK4 ) @ sK2 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f70,f32]) ).
thf(f70,plain,
( ( $false
= ( in @ ( sK6 @ sK4 ) @ sK2 ) )
| ( $false
= ( in @ sK4 @ sK0 ) ) ),
inference(equality_resolution,[status(thm)],[f68]) ).
thf(f68,plain,
! [X0: $i] :
( ( sK4 != X0 )
| ( ( in @ X0 @ sK0 )
= $false )
| ( $false
= ( in @ ( sK6 @ X0 ) @ sK2 ) ) ),
inference(superposition,[status(thm)],[f36,f57]) ).
thf(f57,plain,
! [X1: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ ( sK6 @ X1 ) )
= X1 )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( ( ( ap @ sK2 @ sK0 @ sK1 @ ( sK6 @ X1 ) )
= X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f36,plain,
! [X1: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ X1 )
!= sK4 )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( $false
= ( ( ap @ sK2 @ sK0 @ sK1 @ X1 )
= sK4 ) )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( $false
= ( ( ( ap @ sK2 @ sK0 @ sK1 @ X1 )
= sK4 )
& ( in @ X1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y0 )
= sK4 )
& ( in @ Y0 @ sK2 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y0 )
= sK4 )
& ( in @ Y0 @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
= ( ( in @ sK4 @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y0 )
= sK4 )
& ( in @ Y0 @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y1 )
= Y0 )
& ( in @ Y1 @ sK2 ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ Y1 )
= Y0 )
& ( in @ Y1 @ sK2 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 )
& ( in @ Y4 @ Y0 ) ) ) ) )
@ sK2
@ sK0
@ sK1 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f22,f18]) ).
thf(f22,plain,
( $true
!= ( surjective @ sK2 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f32,plain,
( $true
= ( in @ sK4 @ sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU802^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:34:29 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SEU802^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.46 % Domain : Set Theory
% 0.26/0.46 % Problem : More about Functions - Surjective Functions
% 0.26/0.46 % Version : Especial > Reduced > Especial.
% 0.26/0.46 % English : (! x:i.! y:i.! f:i.in f (surjFuncSet x y) -> surjective x y f)
% 0.26/0.46
% 0.26/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.46 % Source : [Bro08]
% 0.26/0.46 % Names : ZFC304l [Bro08]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.3.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.26/0.46 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.26/0.46 % Number of atoms : 13 ( 4 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.26/0.46 % Number of connectives : 33 ( 0 ~; 0 |; 1 &; 28 @)
% 0.26/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 9 ( 3 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 8 ( 7 usr; 1 con; 0-4 aty)
% 0.26/0.46 % Number of variables : 15 ( 7 ^; 7 !; 1 ?; 15 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : http://mathgate.info/detsetitem.php?id=485
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(in_type,type,
% 0.26/0.46 in: $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(dsetconstr_type,type,
% 0.26/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.26/0.46
% 0.26/0.46 thf(dsetconstrER_type,type,
% 0.26/0.46 dsetconstrER: $o ).
% 0.26/0.46
% 0.26/0.46 thf(dsetconstrER,definition,
% 0.26/0.46 ( dsetconstrER
% 0.26/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.26/0.46 ( ( in @ Xx
% 0.26/0.46 @ ( dsetconstr @ A
% 0.26/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.26/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(funcSet_type,type,
% 0.26/0.46 funcSet: $i > $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(ap_type,type,
% 0.26/0.46 ap: $i > $i > $i > $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(surjective_type,type,
% 0.26/0.46 surjective: $i > $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(surjective,definition,
% 0.26/0.46 ( surjective
% 0.26/0.46 = ( ^ [A: $i,B: $i,Xf: $i] :
% 0.26/0.46 ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ B )
% 0.26/0.46 => ? [Xy: $i] :
% 0.26/0.46 ( ( in @ Xy @ A )
% 0.26/0.46 & ( ( ap @ A @ B @ Xf @ Xy )
% 0.26/0.46 = Xx ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(surjFuncSet_type,type,
% 0.26/0.46 surjFuncSet: $i > $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(surjFuncSet,definition,
% 0.26/0.46 ( surjFuncSet
% 0.26/0.46 = ( ^ [A: $i,B: $i] :
% 0.26/0.46 ( dsetconstr @ ( funcSet @ A @ B )
% 0.26/0.46 @ ^ [Xf: $i] : ( surjective @ A @ B @ Xf ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(surjFuncSetFuncSurj,conjecture,
% 0.26/0.46 ( dsetconstrER
% 0.26/0.46 => ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.26/0.46 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 0.26/0.46 => ( surjective @ Xx @ Xy @ Xf ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.53/1.25 ---- Embedded in THF ---
% 1.53/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.25 %%% Generated on Tue Feb 24 12:34:30 EST 2026
% 1.53/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.25 %%% Logic specification used:
% 1.53/1.25 %%% thf(spec, logic, $$dhol).
% 1.53/1.25
% 1.53/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2DTF26111.p
% See solution above
% 1.53/1.25 ------------------------
% 1.53/1.27 ---- Cleaned THF ---
% 1.53/1.27 thf(in_type,type,
% 1.53/1.27 in: $i > $i > $o ).
% 1.53/1.27
% 1.53/1.27 thf(dsetconstr_type,type,
% 1.53/1.27 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.53/1.27
% 1.53/1.27 thf(dsetconstrER_type,type,
% 1.53/1.27 dsetconstrER: $o ).
% 1.53/1.27
% 1.53/1.27 thf(dsetconstrER,definition,
% 1.53/1.27 ( dsetconstrER
% 1.53/1.27 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.53/1.27 ( ( in @ Xx
% 1.53/1.27 @ ( dsetconstr @ A
% 1.53/1.27 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.53/1.27 => ( Xphi @ Xx ) ) ) ) ).
% 1.53/1.27
% 1.53/1.27 thf(funcSet_type,type,
% 1.53/1.27 funcSet: $i > $i > $i ).
% 1.53/1.27
% 1.53/1.27 thf(ap_type,type,
% 1.53/1.27 ap: $i > $i > $i > $i > $i ).
% 1.53/1.27
% 1.53/1.27 thf(surjective_type,type,
% 1.53/1.27 surjective: $i > $i > $i > $o ).
% 1.53/1.27
% 1.53/1.27 thf(surjective,definition,
% 1.53/1.27 ( surjective
% 1.53/1.27 = ( ^ [A: $i,B: $i,Xf: $i] :
% 1.53/1.27 ! [Xx: $i] :
% 1.53/1.27 ( ( in @ Xx @ B )
% 1.53/1.27 => ? [Xy: $i] :
% 1.53/1.27 ( ( in @ Xy @ A )
% 1.53/1.27 & ( ( ap @ A @ B @ Xf @ Xy )
% 1.53/1.27 = Xx ) ) ) ) ) ).
% 1.53/1.27
% 1.53/1.27 thf(surjFuncSet_type,type,
% 1.53/1.27 surjFuncSet: $i > $i > $i ).
% 1.53/1.27
% 1.53/1.27 thf(surjFuncSet,definition,
% 1.53/1.27 ( surjFuncSet
% 1.53/1.27 = ( ^ [A: $i,B: $i] :
% 1.53/1.27 ( dsetconstr @ ( funcSet @ A @ B )
% 1.53/1.27 @ ^ [Xf: $i] : ( surjective @ A @ B @ Xf ) ) ) ) ).
% 1.53/1.27
% 1.53/1.27 thf(surjFuncSetFuncSurj,conjecture,
% 1.53/1.27 ( dsetconstrER
% 1.53/1.27 => ! [Xx: $i,Xy: $i,Xf: $i] :
% 1.53/1.27 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 1.53/1.27 => ( surjective @ Xx @ Xy @ Xf ) ) ) ).
% 1.53/1.27 ------------------------
% 1.53/1.28 % (26386)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_26111 for (2999ds/2Mi)
% 1.53/1.28 % (26386)Instruction limit reached!
% 1.53/1.28 % (26386)------------------------------
% 1.53/1.28 % (26386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (26386)Termination reason: Unknown
% 1.53/1.28 % (26386)Termination phase: shuffling
% 1.53/1.28
% 1.53/1.28 % (26386)Memory used [KB]: 895
% 1.53/1.28 % (26386)Time elapsed: 0.002 s
% 1.53/1.28 % (26386)Instructions burned: 2 (million)
% 1.53/1.28 % (26386)------------------------------
% 1.53/1.28 % (26386)------------------------------
% 1.53/1.28 % (26384)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_26111 for (2999ds/27Mi)
% 1.53/1.29 % (26384)First to succeed.
% 1.53/1.29 % (26384)Refutation found. Thanks to Tanya!
% 1.53/1.29 % SZS status Theorem for DTF2THF_26111
% 1.53/1.29 % SZS output start Proof for DTF2THF_26111
% 1.53/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.53/1.29 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.53/1.29 thf(func_def_4, type, funcSet: $i > $i > $i).
% 1.53/1.29 thf(func_def_5, type, ap: $i > $i > $i > $i > $i).
% 1.53/1.29 thf(func_def_6, type, surjective: $i > $i > $i > $o).
% 1.53/1.29 thf(func_def_7, type, surjFuncSet: $i > $i > $i).
% 1.53/1.29 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.53/1.29 thf(func_def_27, type, ph5: !>[X0: $tType]:(X0)).
% 1.53/1.29 thf(func_def_28, type, sK6: $i > $i).
% 1.53/1.29 thf(func_def_29, type, sK7: $i > $i).
% 1.53/1.29 thf(f85,plain,(
% 1.53/1.29 $false),
% 1.53/1.29 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.53/1.29 thf(f84,plain,(
% 1.53/1.29 ($false = $true)),
% 1.53/1.29 inference(backward_demodulation,[status(thm)],[f32,f75])).
% 1.53/1.29 thf(f75,plain,(
% 1.53/1.29 ($false = (in @ sK4 @ sK0))),
% 1.53/1.29 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.53/1.29 thf(f73,plain,(
% 1.53/1.29 ($false = $true) | ($false = (in @ sK4 @ sK0))),
% 1.53/1.29 inference(superposition,[status(thm)],[f72,f55])).
% 1.53/1.29 thf(f55,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (((in @ (sK6 @ X1) @ sK2) = $true) | ($false = (in @ X1 @ sK0))) )),
% 1.53/1.29 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.53/1.29 thf(f54,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($false = (in @ X1 @ sK0)) | ((((ap @ sK2 @ sK0 @ sK1 @ (sK6 @ X1)) = X1) & (in @ (sK6 @ X1) @ sK2)) = $true)) )),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.53/1.29 thf(f53,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($false = (in @ X1 @ sK0)) | ($true = ((^[Y0 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y0) = X1) & (in @ Y0 @ sK2))) @ (sK6 @ X1)))) )),
% 1.53/1.29 inference(sigma_clausification,[status(thm)],[f52])).
% 1.53/1.29 thf(f52,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y0) = X1) & (in @ Y0 @ sK2))))) | ($false = (in @ X1 @ sK0))) )),
% 1.53/1.29 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.53/1.29 thf(f51,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK0) => (?? @ $i @ (^[Y0 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y0) = X1) & (in @ Y0 @ sK2))))))) )),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.53/1.29 thf(f50,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK0) => (?? @ $i @ (^[Y1 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y1) = Y0) & (in @ Y1 @ sK2)))))) @ X1))) )),
% 1.53/1.29 inference(pi_clausification,[status(thm)],[f49])).
% 1.53/1.29 thf(f49,plain,(
% 1.53/1.29 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (?? @ $i @ (^[Y1 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y1) = Y0) & (in @ Y1 @ sK2))))))) = $true)),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.53/1.29 thf(f48,plain,(
% 1.53/1.29 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (?? @ $i @ (^[Y2 : $i]: (((ap @ sK2 @ sK0 @ Y0 @ Y2) = Y1) & (in @ Y2 @ sK2)))))))) @ sK1) = $true)),
% 1.53/1.29 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.53/1.29 thf(f46,plain,(
% 1.53/1.29 ($false = $true) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (?? @ $i @ (^[Y2 : $i]: (((ap @ sK2 @ sK0 @ Y0 @ Y2) = Y1) & (in @ Y2 @ sK2)))))))) @ sK1) = $true)),
% 1.53/1.29 inference(superposition,[status(thm)],[f37,f45])).
% 1.53/1.29 thf(f45,plain,(
% 1.53/1.29 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($false = (in @ X2 @ (dsetconstr @ X1 @ X3))) | ((X3 @ X2) = $true)) )),
% 1.53/1.29 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.53/1.29 thf(f44,plain,(
% 1.53/1.29 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ (dsetconstr @ X1 @ X3)) => (X3 @ X2)))) )),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.53/1.29 thf(f43,plain,(
% 1.53/1.29 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ X2))) @ X3) = $true)) )),
% 1.53/1.29 inference(pi_clausification,[status(thm)],[f42])).
% 1.53/1.29 thf(f42,plain,(
% 1.53/1.29 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ X2)))))) )),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.53/1.29 thf(f41,plain,(
% 1.53/1.29 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (Y1 @ Y0))))) @ X2))) )),
% 1.53/1.29 inference(pi_clausification,[status(thm)],[f40])).
% 1.53/1.29 thf(f40,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (Y1 @ Y0)))))))) )),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.53/1.29 thf(f39,plain,(
% 1.53/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1))))))) @ X1) = $true)) )),
% 1.53/1.29 inference(pi_clausification,[status(thm)],[f38])).
% 1.53/1.29 thf(f38,plain,(
% 1.53/1.29 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))))),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.53/1.29 thf(f27,plain,(
% 1.53/1.29 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))) = $true)),
% 1.53/1.29 inference(definition_unfolding,[status(thm)],[f21,f19])).
% 1.53/1.29 thf(f19,plain,(
% 1.53/1.29 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 1.53/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.53/1.29 thf(f14,plain,(
% 1.53/1.29 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 1.53/1.29 inference(fool_elimination,[status(thm)],[f13])).
% 1.53/1.29 thf(f13,plain,(
% 1.53/1.29 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X1)) = dsetconstrER)),
% 1.53/1.29 inference(rectify,[status(thm)],[f1])).
% 1.53/1.29 thf(f1,axiom,(
% 1.53/1.29 (! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.53/1.29 file('/export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2THF_26111.p',dsetconstrER)).
% 1.53/1.29 thf(f21,plain,(
% 1.53/1.29 (dsetconstrER = $true)),
% 1.53/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.53/1.29 thf(f17,plain,(
% 1.53/1.29 (((in @ sK1 @ (surjFuncSet @ sK2 @ sK0)) = $true) & ($true != (surjective @ sK2 @ sK0 @ sK1))) & (dsetconstrER = $true)),
% 1.53/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16])).
% 1.53/1.29 thf(f16,plain,(
% 1.53/1.29 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (surjFuncSet @ X2 @ X0))) & ($true != (surjective @ X2 @ X0 @ X1))) => (((in @ sK1 @ (surjFuncSet @ sK2 @ sK0)) = $true) & ($true != (surjective @ sK2 @ sK0 @ sK1)))),
% 1.53/1.29 introduced(definition,[],[choice_axiom])).
% 1.53/1.29 thf(f15,plain,(
% 1.53/1.29 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (surjFuncSet @ X2 @ X0))) & ($true != (surjective @ X2 @ X0 @ X1))) & (dsetconstrER = $true)),
% 1.53/1.29 inference(ennf_transformation,[status(thm)],[f8])).
% 1.53/1.29 thf(f8,plain,(
% 1.53/1.29 ~((dsetconstrER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (surjFuncSet @ X2 @ X0))) => ($true = (surjective @ X2 @ X0 @ X1))))),
% 1.53/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.53/1.29 thf(f7,plain,(
% 1.53/1.29 ~(dsetconstrER => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (surjFuncSet @ X2 @ X0)) => (surjective @ X2 @ X0 @ X1)))),
% 1.53/1.29 inference(rectify,[status(thm)],[f5])).
% 1.53/1.29 thf(f5,negated_conjecture,(
% 1.53/1.29 ~(dsetconstrER => ! [X3 : $i,X5 : $i,X2 : $i] : ((in @ X5 @ (surjFuncSet @ X2 @ X3)) => (surjective @ X2 @ X3 @ X5)))),
% 1.53/1.29 inference(negated_conjecture,[status(cth)],[f4])).
% 1.53/1.29 thf(f4,conjecture,(
% 1.53/1.29 dsetconstrER => ! [X3 : $i,X5 : $i,X2 : $i] : ((in @ X5 @ (surjFuncSet @ X2 @ X3)) => (surjective @ X2 @ X3 @ X5))),
% 1.53/1.29 file('/export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2THF_26111.p',surjFuncSetFuncSurj)).
% 1.53/1.29 thf(f37,plain,(
% 1.53/1.29 ((in @ sK1 @ (dsetconstr @ (funcSet @ sK2 @ sK0) @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (?? @ $i @ (^[Y2 : $i]: (((ap @ sK2 @ sK0 @ Y0 @ Y2) = Y1) & (in @ Y2 @ sK2)))))))))) = $true)),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.53/1.29 thf(f25,plain,(
% 1.53/1.29 ($true = (in @ sK1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) => (?? @ $i @ (^[Y7 : $i]: (((ap @ Y3 @ Y4 @ Y5 @ Y7) = Y6) & (in @ Y7 @ Y3)))))))))))) @ Y0 @ Y1 @ Y2)))))) @ sK2 @ sK0)))),
% 1.53/1.29 inference(definition_unfolding,[status(thm)],[f23,f24])).
% 1.53/1.29 thf(f24,plain,(
% 1.53/1.29 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) => (?? @ $i @ (^[Y7 : $i]: (((ap @ Y3 @ Y4 @ Y5 @ Y7) = Y6) & (in @ Y7 @ Y3)))))))))))) @ Y0 @ Y1 @ Y2)))))))),
% 1.53/1.29 inference(definition_unfolding,[status(thm)],[f20,f18])).
% 1.53/1.29 thf(f18,plain,(
% 1.53/1.29 (surjective = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3) & (in @ Y4 @ Y0)))))))))))))),
% 1.53/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.29 thf(f12,plain,(
% 1.53/1.29 (surjective = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3) & (in @ Y4 @ Y0)))))))))))))),
% 1.53/1.29 inference(fool_elimination,[status(thm)],[f11])).
% 1.53/1.29 thf(f11,plain,(
% 1.53/1.29 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => ? [X4 : $i] : ((in @ X4 @ X0) & ((ap @ X0 @ X1 @ X2 @ X4) = X3))))) = surjective)),
% 1.53/1.29 inference(rectify,[status(thm)],[f2])).
% 1.53/1.29 thf(f2,axiom,(
% 1.53/1.29 ((^[X0 : $i, X4 : $i, X5 : $i] : (! [X2 : $i] : ((in @ X2 @ X4) => ? [X3 : $i] : ((in @ X3 @ X0) & ((ap @ X0 @ X4 @ X5 @ X3) = X2))))) = surjective)),
% 1.53/1.29 file('/export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2THF_26111.p',surjective)).
% 1.53/1.29 thf(f20,plain,(
% 1.53/1.29 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))))),
% 1.53/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.29 thf(f10,plain,(
% 1.53/1.29 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))))),
% 1.53/1.29 inference(fool_elimination,[status(thm)],[f9])).
% 1.53/1.29 thf(f9,plain,(
% 1.53/1.29 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (funcSet @ X0 @ X1) @ (^[X2 : $i] : (surjective @ X0 @ X1 @ X2)))) = surjFuncSet)),
% 1.53/1.29 inference(rectify,[status(thm)],[f3])).
% 1.53/1.29 thf(f3,axiom,(
% 1.53/1.29 ((^[X0 : $i, X4 : $i] : (dsetconstr @ (funcSet @ X0 @ X4) @ (^[X5 : $i] : (surjective @ X0 @ X4 @ X5)))) = surjFuncSet)),
% 1.53/1.29 file('/export/starexec/sandbox2/tmp/tmp.XSU7L56QIm/DTF2THF_26111.p',surjFuncSet)).
% 1.53/1.29 thf(f23,plain,(
% 1.53/1.29 ((in @ sK1 @ (surjFuncSet @ sK2 @ sK0)) = $true)),
% 1.53/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.53/1.29 thf(f72,plain,(
% 1.53/1.29 ($false = (in @ (sK6 @ sK4) @ sK2))),
% 1.53/1.29 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.53/1.29 thf(f71,plain,(
% 1.53/1.29 ($false = (in @ (sK6 @ sK4) @ sK2)) | ($false = $true)),
% 1.53/1.29 inference(forward_demodulation,[status(thm)],[f70,f32])).
% 1.53/1.29 thf(f70,plain,(
% 1.53/1.29 ($false = (in @ (sK6 @ sK4) @ sK2)) | ($false = (in @ sK4 @ sK0))),
% 1.53/1.29 inference(equality_resolution,[status(thm)],[f68])).
% 1.53/1.29 thf(f68,plain,(
% 1.53/1.29 ( ! [X0 : $i] : ((sK4 != X0) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (sK6 @ X0) @ sK2))) )),
% 1.53/1.29 inference(superposition,[status(thm)],[f36,f57])).
% 1.53/1.29 thf(f57,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (((ap @ sK2 @ sK0 @ sK1 @ (sK6 @ X1)) = X1) | ($false = (in @ X1 @ sK0))) )),
% 1.53/1.29 inference(equality_proxy_clausification,[status(thm)],[f56])).
% 1.53/1.29 thf(f56,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($false = (in @ X1 @ sK0)) | (((ap @ sK2 @ sK0 @ sK1 @ (sK6 @ X1)) = X1) = $true)) )),
% 1.53/1.29 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.53/1.29 thf(f36,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (((ap @ sK2 @ sK0 @ sK1 @ X1) != sK4) | ($false = (in @ X1 @ sK2))) )),
% 1.53/1.29 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.53/1.29 thf(f35,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($false = ((ap @ sK2 @ sK0 @ sK1 @ X1) = sK4)) | ($false = (in @ X1 @ sK2))) )),
% 1.53/1.29 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.53/1.29 thf(f34,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($false = (((ap @ sK2 @ sK0 @ sK1 @ X1) = sK4) & (in @ X1 @ sK2)))) )),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.53/1.29 thf(f33,plain,(
% 1.53/1.29 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y0) = sK4) & (in @ Y0 @ sK2))) @ X1))) )),
% 1.53/1.29 inference(pi_clausification,[status(thm)],[f31])).
% 1.53/1.29 thf(f31,plain,(
% 1.53/1.29 ($false = (?? @ $i @ (^[Y0 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y0) = sK4) & (in @ Y0 @ sK2)))))),
% 1.53/1.29 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.53/1.29 thf(f30,plain,(
% 1.53/1.29 ($false = ((in @ sK4 @ sK0) => (?? @ $i @ (^[Y0 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y0) = sK4) & (in @ Y0 @ sK2))))))),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.53/1.29 thf(f29,plain,(
% 1.53/1.29 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK0) => (?? @ $i @ (^[Y1 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y1) = Y0) & (in @ Y1 @ sK2)))))) @ sK4))),
% 1.53/1.29 inference(sigma_clausification,[status(thm)],[f28])).
% 1.53/1.29 thf(f28,plain,(
% 1.53/1.29 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (?? @ $i @ (^[Y1 : $i]: (((ap @ sK2 @ sK0 @ sK1 @ Y1) = Y0) & (in @ Y1 @ sK2))))))) != $true)),
% 1.53/1.29 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.53/1.29 thf(f26,plain,(
% 1.53/1.29 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3) & (in @ Y4 @ Y0)))))))))))) @ sK2 @ sK0 @ sK1) != $true)),
% 1.53/1.29 inference(definition_unfolding,[status(thm)],[f22,f18])).
% 1.53/1.29 thf(f22,plain,(
% 1.53/1.29 ($true != (surjective @ sK2 @ sK0 @ sK1))),
% 1.53/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.53/1.29 thf(f32,plain,(
% 1.53/1.29 ($true = (in @ sK4 @ sK0))),
% 1.53/1.29 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.53/1.29 % SZS output end Proof for DTF2THF_26111
% 1.53/1.29 % (26384)------------------------------
% 1.53/1.29 % (26384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (26384)Termination reason: Refutation
% 1.53/1.29
% 1.53/1.29 % (26384)Memory used [KB]: 5628
% 1.53/1.29 % (26384)Time elapsed: 0.006 s
% 1.53/1.29 % (26384)Instructions burned: 10 (million)
% 1.53/1.29 % (26384)------------------------------
% 1.53/1.29 % (26384)------------------------------
% 1.53/1.29 % (26381)Success in time 0.017 s
%------------------------------------------------------------------------------