%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU803^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 1.41s 1.13s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 379 ( 100 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 512 ( 42 ~; 27 |; 33 &; 369 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 9 usr; 8 con; 0-4 aty)
% ( 4 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 98 ( 28 ^; 50 !; 20 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
funcSet: $i > $i > $i ).
thf(func_def_2,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_3,type,
surjective: $i > $i > $i > $o ).
thf(func_def_18,type,
sK0: $i > $i ).
thf(f38,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true != $true )
| ( sK5 != sK5 ) ),
inference(superposition,[status(thm)],[f36,f25]) ).
thf(f25,plain,
( $true
= ( in @ sK5 @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $false
= ( ( in @ sK5 @ sK1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
& ( ( ap @ sK2 @ sK1 @ sK3 @ Y0 )
= sK5 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
& ( ( ap @ sK2 @ sK1 @ sK3 @ Y1 )
= Y0 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
& ( ( ap @ sK2 @ sK1 @ sK3 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) )
@ sK2
@ sK1
@ sK3 ) ),
inference(definition_unfolding,[status(thm)],[f16,f19]) ).
thf(f19,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) ) ) )
= surjective ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) ) ) )
= surjective ),
file('/export/starexec/sandbox/tmp/tmp.LY66uYPnul/DTF2THF_18143.p',surjective) ).
thf(f16,plain,
( $true
!= ( surjective @ sK2 @ sK1 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( in @ sK3 @ ( funcSet @ sK2 @ sK1 ) )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ sK1 )
!= $true )
| ( ( ap @ sK2 @ sK1 @ sK3 @ ( sK0 @ X4 ) )
= X4 ) )
& ( $true
!= ( surjective @ sK2 @ sK1 @ sK3 ) )
& ! [X5: $i] :
( ( ( in @ ( sK0 @ X5 ) @ sK2 )
= $true )
| ( ( in @ X5 @ sK1 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f13,f12]) ).
thf(f12,plain,
( ? [X0: $i > $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( funcSet @ X2 @ X1 ) ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X1 ) )
| ( ( ap @ X2 @ X1 @ X3 @ ( X0 @ X4 ) )
= X4 ) )
& ( $true
!= ( surjective @ X2 @ X1 @ X3 ) ) )
& ! [X5: $i] :
( ( $true
= ( in @ ( X0 @ X5 ) @ X2 ) )
| ( ( in @ X5 @ X1 )
!= $true ) ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ ( funcSet @ sK2 @ sK1 ) )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ sK1 )
!= $true )
| ( ( ap @ sK2 @ sK1 @ X3 @ ( sK0 @ X4 ) )
= X4 ) )
& ( $true
!= ( surjective @ sK2 @ sK1 @ X3 ) ) )
& ! [X5: $i] :
( ( ( in @ ( sK0 @ X5 ) @ sK2 )
= $true )
| ( ( in @ X5 @ sK1 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( funcSet @ sK2 @ sK1 ) )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ sK1 )
!= $true )
| ( ( ap @ sK2 @ sK1 @ X3 @ ( sK0 @ X4 ) )
= X4 ) )
& ( $true
!= ( surjective @ sK2 @ sK1 @ X3 ) ) )
=> ( ( ( in @ sK3 @ ( funcSet @ sK2 @ sK1 ) )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ sK1 )
!= $true )
| ( ( ap @ sK2 @ sK1 @ sK3 @ ( sK0 @ X4 ) )
= X4 ) )
& ( $true
!= ( surjective @ sK2 @ sK1 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: $i > $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( funcSet @ X2 @ X1 ) ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X1 ) )
| ( ( ap @ X2 @ X1 @ X3 @ ( X0 @ X4 ) )
= X4 ) )
& ( $true
!= ( surjective @ X2 @ X1 @ X3 ) ) )
& ! [X5: $i] :
( ( $true
= ( in @ ( X0 @ X5 ) @ X2 ) )
| ( ( in @ X5 @ X1 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X0: $i > $i,X1: $i,X2: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ ( funcSet @ X2 @ X1 ) ) )
& ! [X5: $i] :
( ( ( in @ X5 @ X1 )
!= $true )
| ( ( ap @ X2 @ X1 @ X4 @ ( X0 @ X5 ) )
= X5 ) )
& ( $true
!= ( surjective @ X2 @ X1 @ X4 ) ) )
& ! [X3: $i] :
( ( ( in @ ( X0 @ X3 ) @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: $i > $i,X1: $i,X2: $i] :
( ? [X4: $i] :
( ( $true
!= ( surjective @ X2 @ X1 @ X4 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ X1 )
!= $true )
| ( ( ap @ X2 @ X1 @ X4 @ ( X0 @ X5 ) )
= X5 ) )
& ( $true
= ( in @ X4 @ ( funcSet @ X2 @ X1 ) ) ) )
& ! [X3: $i] :
( ( ( in @ ( X0 @ X3 ) @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i > $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ ( X0 @ X3 ) @ X2 )
= $true ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ ( funcSet @ X2 @ X1 ) ) )
=> ( ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( ap @ X2 @ X1 @ X4 @ ( X0 @ X5 ) )
= X5 ) )
=> ( $true
= ( surjective @ X2 @ X1 @ X4 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( X0 @ X3 ) @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X2 @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( ap @ X2 @ X1 @ X4 @ ( X0 @ X5 ) )
= X5 ) )
=> ( surjective @ X2 @ X1 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X2: $i > $i,X0: $i,X1: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( funcSet @ X1 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X1 @ X0 @ X5 @ ( X2 @ X3 ) )
= X3 ) )
=> ( surjective @ X1 @ X0 @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X2: $i > $i,X0: $i,X1: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( funcSet @ X1 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X1 @ X0 @ X5 @ ( X2 @ X3 ) )
= X3 ) )
=> ( surjective @ X1 @ X0 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LY66uYPnul/DTF2THF_18143.p',leftInvIsSurj) ).
thf(f36,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK1 )
!= $true )
| ( sK5 != X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK1 )
!= $true )
| ( sK5 != X0 )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK1 )
!= $true )
| ( $false = $true )
| ( ( in @ X0 @ sK1 )
!= $true )
| ( sK5 != X0 ) ),
inference(superposition,[status(thm)],[f15,f30]) ).
thf(f30,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK0 @ X0 ) @ sK2 ) )
| ( sK5 != X0 )
| ( ( in @ X0 @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f29,f17]) ).
thf(f17,plain,
! [X4: $i] :
( ( ( ap @ sK2 @ sK1 @ sK3 @ ( sK0 @ X4 ) )
= X4 )
| ( ( in @ X4 @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f29,plain,
! [X1: $i] :
( ( sK5
!= ( ap @ sK2 @ sK1 @ sK3 @ X1 ) )
| ( ( in @ X1 @ sK2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
= $false )
| ( ( ( ap @ sK2 @ sK1 @ sK3 @ X1 )
= sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
& ( ( ap @ sK2 @ sK1 @ sK3 @ X1 )
= sK5 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
& ( ( ap @ sK2 @ sK1 @ sK3 @ Y0 )
= sK5 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
& ( ( ap @ sK2 @ sK1 @ sK3 @ Y0 )
= sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f15,plain,
! [X5: $i] :
( ( ( in @ ( sK0 @ X5 ) @ sK2 )
= $true )
| ( ( in @ X5 @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU803^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.08 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.27 % Computer : n020.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8042.1875MB
% 0.10/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Feb 24 12:34:42 EST 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 ---- Original DTF file ---
% 0.10/0.35 thf(spec,logic,$$dhol).
% 0.10/0.35 %------------------------------------------------------------------------------
% 0.10/0.35 % File : SEU803^2 : TPTP v9.2.1. Released v3.7.0.
% 0.10/0.35 % Domain : Set Theory
% 0.10/0.35 % Problem : More about Functions - Surjective Functions
% 0.10/0.35 % Version : Especial > Reduced > Especial.
% 0.10/0.35 % English : (! A:i.! B:i.! f:i>i.(! x:i.in x A -> in (f x) B) ->
% 0.10/0.35 % (! g:i.in g (funcSet B A) -> (! x:i.in x A ->
% 0.10/0.35 % ap B A g (f x) = x) -> surjective B A g))
% 0.10/0.35
% 0.10/0.35 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.10/0.35 % Source : [Bro08]
% 0.10/0.35 % Names : ZFC305l [Bro08]
% 0.10/0.35
% 0.10/0.35 % Status : Theorem
% 0.10/0.35 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.10/0.35 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.10/0.35 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.10/0.35 % Maximal formula atoms : 6 ( 5 avg)
% 0.10/0.35 % Number of connectives : 34 ( 0 ~; 0 |; 1 &; 27 @)
% 0.10/0.35 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.10/0.35 % Maximal formula depth : 12 ( 7 avg)
% 0.10/0.35 % Number of types : 2 ( 0 usr)
% 0.10/0.35 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.10/0.35 % Number of symbols : 5 ( 4 usr; 0 con; 2-4 aty)
% 0.10/0.35 % Number of variables : 11 ( 3 ^; 7 !; 1 ?; 11 :)
% 0.10/0.35 % SPC : TH0_THM_EQU_NAR
% 0.10/0.35
% 0.10/0.35 % Comments : http://mathgate.info/detsetitem.php?id=486
% 0.10/0.35 %------------------------------------------------------------------------------
% 0.10/0.35 thf(in_type,type,
% 0.10/0.35 in: $i > $i > $o ).
% 0.10/0.35
% 0.10/0.35 thf(funcSet_type,type,
% 0.10/0.35 funcSet: $i > $i > $i ).
% 0.10/0.35
% 0.10/0.35 thf(ap_type,type,
% 0.10/0.35 ap: $i > $i > $i > $i > $i ).
% 0.10/0.35
% 0.10/0.35 thf(surjective_type,type,
% 0.10/0.35 surjective: $i > $i > $i > $o ).
% 0.10/0.35
% 0.10/0.35 thf(surjective,definition,
% 0.10/0.35 ( surjective
% 0.10/0.35 = ( ^ [A: $i,B: $i,Xf: $i] :
% 0.10/0.35 ! [Xx: $i] :
% 0.10/0.35 ( ( in @ Xx @ B )
% 0.10/0.35 => ? [Xy: $i] :
% 0.10/0.35 ( ( in @ Xy @ A )
% 0.10/0.35 & ( ( ap @ A @ B @ Xf @ Xy )
% 0.10/0.35 = Xx ) ) ) ) ) ).
% 0.10/0.35
% 0.10/0.35 thf(leftInvIsSurj,conjecture,
% 0.10/0.35 ! [A: $i,B: $i,Xf: $i > $i] :
% 0.10/0.35 ( ! [Xx: $i] :
% 0.10/0.35 ( ( in @ Xx @ A )
% 0.10/0.35 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.10/0.35 => ! [Xg: $i] :
% 0.10/0.35 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 0.10/0.35 => ( ! [Xx: $i] :
% 0.10/0.35 ( ( in @ Xx @ A )
% 0.10/0.35 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 0.10/0.35 = Xx ) )
% 0.10/0.35 => ( surjective @ B @ A @ Xg ) ) ) ) ).
% 0.10/0.35
% 0.10/0.35 %------------------------------------------------------------------------------
% 0.10/0.35 ------------------------
% 1.25/1.10 ---- Embedded in THF ---
% 1.25/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.25/1.10 %%% Generated on Tue Feb 24 12:34:42 EST 2026
% 1.25/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.25/1.10 %%% Logic specification used:
% 1.25/1.10 %%% thf(spec, logic, $$dhol).
% 1.25/1.10
% 1.25/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LY66uYPnul/DTF2DTF18143.p
% See solution above
% 1.25/1.10 ------------------------
% 1.25/1.11 ---- Cleaned THF ---
% 1.25/1.11 thf(in_type,type,
% 1.25/1.11 in: $i > $i > $o ).
% 1.25/1.11
% 1.25/1.11 thf(funcSet_type,type,
% 1.25/1.11 funcSet: $i > $i > $i ).
% 1.25/1.11
% 1.25/1.11 thf(ap_type,type,
% 1.25/1.11 ap: $i > $i > $i > $i > $i ).
% 1.25/1.11
% 1.25/1.11 thf(surjective_type,type,
% 1.25/1.11 surjective: $i > $i > $i > $o ).
% 1.25/1.11
% 1.25/1.11 thf(surjective,definition,
% 1.25/1.11 ( surjective
% 1.25/1.11 = ( ^ [A: $i,B: $i,Xf: $i] :
% 1.25/1.11 ! [Xx: $i] :
% 1.25/1.11 ( ( in @ Xx @ B )
% 1.25/1.11 => ? [Xy: $i] :
% 1.25/1.11 ( ( in @ Xy @ A )
% 1.25/1.11 & ( ( ap @ A @ B @ Xf @ Xy )
% 1.25/1.11 = Xx ) ) ) ) ) ).
% 1.25/1.11
% 1.25/1.11 thf(leftInvIsSurj,conjecture,
% 1.25/1.11 ! [A: $i,B: $i,Xf: $i > $i] :
% 1.25/1.11 ( ! [Xx: $i] :
% 1.25/1.11 ( ( in @ Xx @ A )
% 1.25/1.11 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.25/1.11 => ! [Xg: $i] :
% 1.25/1.11 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 1.25/1.11 => ( ! [Xx: $i] :
% 1.25/1.11 ( ( in @ Xx @ A )
% 1.25/1.11 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 1.25/1.11 = Xx ) )
% 1.25/1.11 => ( surjective @ B @ A @ Xg ) ) ) ) ).
% 1.25/1.11 ------------------------
% 1.25/1.12 % (18434)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_18143 for (2999ds/4Mi)
% 1.25/1.12 % (18436)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18143 for (2999ds/2Mi)
% 1.25/1.12 % (18434)Instruction limit reached!
% 1.25/1.12 % (18434)------------------------------
% 1.25/1.12 % (18434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.12 % (18434)Termination reason: Unknown
% 1.25/1.12 % (18434)Termination phase: Saturation
% 1.25/1.12
% 1.25/1.12 % (18434)Memory used [KB]: 5500
% 1.25/1.12 % (18434)Time elapsed: 0.003 s
% 1.25/1.12 % (18434)Instructions burned: 4 (million)
% 1.25/1.12 % (18434)------------------------------
% 1.25/1.12 % (18434)------------------------------
% 1.25/1.12 % (18436)Instruction limit reached!
% 1.25/1.12 % (18436)------------------------------
% 1.25/1.12 % (18436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.12 % (18436)Termination reason: Unknown
% 1.25/1.12 % (18436)Termination phase: Saturation
% 1.25/1.12
% 1.25/1.12 % (18436)Memory used [KB]: 5500
% 1.25/1.12 % (18436)Time elapsed: 0.002 s
% 1.25/1.12 % (18436)Instructions burned: 3 (million)
% 1.25/1.12 % (18436)------------------------------
% 1.25/1.12 % (18436)------------------------------
% 1.41/1.13 % (18433)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18143 for (2999ds/183Mi)
% 1.41/1.13 % (18435)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_18143 for (2999ds/27Mi)
% 1.41/1.13 % (18437)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_18143 for (2999ds/2Mi)
% 1.41/1.13 % (18438)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_18143 for (2999ds/275Mi)
% 1.41/1.13 % (18439)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18143 for (2999ds/18Mi)
% 1.41/1.13 % (18437)Instruction limit reached!
% 1.41/1.13 % (18437)------------------------------
% 1.41/1.13 % (18437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.13 % (18437)Termination reason: Unknown
% 1.41/1.13 % (18437)Termination phase: Property scanning
% 1.41/1.13
% 1.41/1.13 % (18437)Memory used [KB]: 895
% 1.41/1.13 % (18437)Time elapsed: 0.003 s
% 1.41/1.13 % (18437)Instructions burned: 2 (million)
% 1.41/1.13 % (18437)------------------------------
% 1.41/1.13 % (18437)------------------------------
% 1.41/1.13 % (18438)Refutation not found, incomplete strategy
% 1.41/1.13 % (18438)------------------------------
% 1.41/1.13 % (18438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.13 % (18438)Termination reason: Refutation not found, incomplete strategy
% 1.41/1.13
% 1.41/1.13
% 1.41/1.13 % (18438)Memory used [KB]: 5500
% 1.41/1.13 % (18438)Time elapsed: 0.004 s
% 1.41/1.13 % (18438)Instructions burned: 3 (million)
% 1.41/1.13 % (18438)------------------------------
% 1.41/1.13 % (18438)------------------------------
% 1.41/1.13 % (18441)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_18143 for (2999ds/37Mi)
% 1.41/1.13 % (18433)First to succeed.
% 1.41/1.13 % (18440)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18143 for (2999ds/3Mi)
% 1.41/1.13 % (18440)Instruction limit reached!
% 1.41/1.13 % (18440)------------------------------
% 1.41/1.13 % (18440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.13 % (18440)Termination reason: Unknown
% 1.41/1.13 % (18440)Termination phase: Saturation
% 1.41/1.13
% 1.41/1.13 % (18440)Memory used [KB]: 5500
% 1.41/1.13 % (18440)Time elapsed: 0.003 s
% 1.41/1.13 % (18440)Instructions burned: 3 (million)
% 1.41/1.13 % (18440)------------------------------
% 1.41/1.13 % (18440)------------------------------
% 1.41/1.13 % (18435)Also succeeded, but the first one will report.
% 1.41/1.13 % (18433)Refutation found. Thanks to Tanya!
% 1.41/1.13 % SZS status Theorem for DTF2THF_18143
% 1.41/1.13 % SZS output start Proof for DTF2THF_18143
% 1.41/1.13 thf(func_def_0, type, in: $i > $i > $o).
% 1.41/1.13 thf(func_def_1, type, funcSet: $i > $i > $i).
% 1.41/1.13 thf(func_def_2, type, ap: $i > $i > $i > $i > $i).
% 1.41/1.13 thf(func_def_3, type, surjective: $i > $i > $i > $o).
% 1.41/1.13 thf(func_def_18, type, sK0: $i > $i).
% 1.41/1.13 thf(f38,plain,(
% 1.41/1.13 $false),
% 1.41/1.13 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.41/1.13 thf(f37,plain,(
% 1.41/1.13 ($true != $true) | (sK5 != sK5)),
% 1.41/1.13 inference(superposition,[status(thm)],[f36,f25])).
% 1.41/1.13 thf(f25,plain,(
% 1.41/1.13 ($true = (in @ sK5 @ sK1))),
% 1.41/1.13 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.41/1.13 thf(f23,plain,(
% 1.41/1.13 ($false = ((in @ sK5 @ sK1) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) & ((ap @ sK2 @ sK1 @ sK3 @ Y0) = sK5))))))),
% 1.41/1.13 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.41/1.13 thf(f22,plain,(
% 1.41/1.13 (((^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) & ((ap @ sK2 @ sK1 @ sK3 @ Y1) = Y0)))))) @ sK5) = $false)),
% 1.41/1.13 inference(sigma_clausification,[status(thm)],[f21])).
% 1.41/1.14 thf(f21,plain,(
% 1.41/1.14 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) & ((ap @ sK2 @ sK1 @ sK3 @ Y1) = Y0))))))))),
% 1.41/1.14 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.41/1.14 thf(f20,plain,(
% 1.41/1.14 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3)))))))))))) @ sK2 @ sK1 @ sK3))),
% 1.41/1.14 inference(definition_unfolding,[status(thm)],[f16,f19])).
% 1.41/1.14 thf(f19,plain,(
% 1.41/1.14 (surjective = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3)))))))))))))),
% 1.41/1.14 inference(cnf_transformation,[status(thm)],[f8])).
% 1.41/1.14 thf(f8,plain,(
% 1.41/1.14 (surjective = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3)))))))))))))),
% 1.41/1.14 inference(fool_elimination,[status(thm)],[f7])).
% 1.41/1.14 thf(f7,plain,(
% 1.41/1.14 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => ? [X4 : $i] : (((ap @ X0 @ X1 @ X2 @ X4) = X3) & (in @ X4 @ X0))))) = surjective)),
% 1.41/1.14 inference(rectify,[status(thm)],[f1])).
% 1.41/1.14 thf(f1,axiom,(
% 1.41/1.14 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => ? [X4 : $i] : (((ap @ X0 @ X1 @ X2 @ X4) = X3) & (in @ X4 @ X0))))) = surjective)),
% 1.41/1.14 file('/export/starexec/sandbox/tmp/tmp.LY66uYPnul/DTF2THF_18143.p',surjective)).
% 1.41/1.14 thf(f16,plain,(
% 1.41/1.14 ($true != (surjective @ sK2 @ sK1 @ sK3))),
% 1.41/1.14 inference(cnf_transformation,[status(thm)],[f14])).
% 1.41/1.14 thf(f14,plain,(
% 1.41/1.14 (((in @ sK3 @ (funcSet @ sK2 @ sK1)) = $true) & ! [X4 : $i] : (((in @ X4 @ sK1) != $true) | ((ap @ sK2 @ sK1 @ sK3 @ (sK0 @ X4)) = X4)) & ($true != (surjective @ sK2 @ sK1 @ sK3))) & ! [X5 : $i] : (((in @ (sK0 @ X5) @ sK2) = $true) | ((in @ X5 @ sK1) != $true))),
% 1.41/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f13,f12])).
% 1.41/1.14 thf(f12,plain,(
% 1.41/1.14 ? [X0 : $i > $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (funcSet @ X2 @ X1))) & ! [X4 : $i] : (($true != (in @ X4 @ X1)) | ((ap @ X2 @ X1 @ X3 @ (X0 @ X4)) = X4)) & ($true != (surjective @ X2 @ X1 @ X3))) & ! [X5 : $i] : (($true = (in @ (X0 @ X5) @ X2)) | ((in @ X5 @ X1) != $true))) => (? [X3 : $i] : (((in @ X3 @ (funcSet @ sK2 @ sK1)) = $true) & ! [X4 : $i] : (((in @ X4 @ sK1) != $true) | ((ap @ sK2 @ sK1 @ X3 @ (sK0 @ X4)) = X4)) & ($true != (surjective @ sK2 @ sK1 @ X3))) & ! [X5 : $i] : (((in @ (sK0 @ X5) @ sK2) = $true) | ((in @ X5 @ sK1) != $true)))),
% 1.41/1.14 introduced(definition,[],[choice_axiom])).
% 1.41/1.14 thf(f13,plain,(
% 1.41/1.14 ? [X3 : $i] : (((in @ X3 @ (funcSet @ sK2 @ sK1)) = $true) & ! [X4 : $i] : (((in @ X4 @ sK1) != $true) | ((ap @ sK2 @ sK1 @ X3 @ (sK0 @ X4)) = X4)) & ($true != (surjective @ sK2 @ sK1 @ X3))) => (((in @ sK3 @ (funcSet @ sK2 @ sK1)) = $true) & ! [X4 : $i] : (((in @ X4 @ sK1) != $true) | ((ap @ sK2 @ sK1 @ sK3 @ (sK0 @ X4)) = X4)) & ($true != (surjective @ sK2 @ sK1 @ sK3)))),
% 1.41/1.14 introduced(definition,[],[choice_axiom])).
% 1.41/1.14 thf(f11,plain,(
% 1.41/1.14 ? [X0 : $i > $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (funcSet @ X2 @ X1))) & ! [X4 : $i] : (($true != (in @ X4 @ X1)) | ((ap @ X2 @ X1 @ X3 @ (X0 @ X4)) = X4)) & ($true != (surjective @ X2 @ X1 @ X3))) & ! [X5 : $i] : (($true = (in @ (X0 @ X5) @ X2)) | ((in @ X5 @ X1) != $true)))),
% 1.41/1.14 inference(rectify,[status(thm)],[f10])).
% 1.41/1.14 thf(f10,plain,(
% 1.41/1.14 ? [X0 : $i > $i,X1 : $i,X2 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ (funcSet @ X2 @ X1))) & ! [X5 : $i] : (((in @ X5 @ X1) != $true) | ((ap @ X2 @ X1 @ X4 @ (X0 @ X5)) = X5)) & ($true != (surjective @ X2 @ X1 @ X4))) & ! [X3 : $i] : (((in @ (X0 @ X3) @ X2) = $true) | ((in @ X3 @ X1) != $true)))),
% 1.41/1.14 inference(flattening,[status(thm)],[f9])).
% 1.41/1.14 thf(f9,plain,(
% 1.41/1.14 ? [X0 : $i > $i,X1 : $i,X2 : $i] : (? [X4 : $i] : ((($true != (surjective @ X2 @ X1 @ X4)) & ! [X5 : $i] : (((in @ X5 @ X1) != $true) | ((ap @ X2 @ X1 @ X4 @ (X0 @ X5)) = X5))) & ($true = (in @ X4 @ (funcSet @ X2 @ X1)))) & ! [X3 : $i] : (((in @ (X0 @ X3) @ X2) = $true) | ((in @ X3 @ X1) != $true)))),
% 1.41/1.14 inference(ennf_transformation,[status(thm)],[f6])).
% 1.41/1.14 thf(f6,plain,(
% 1.41/1.14 ~! [X0 : $i > $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) = $true) => ((in @ (X0 @ X3) @ X2) = $true)) => ! [X4 : $i] : (($true = (in @ X4 @ (funcSet @ X2 @ X1))) => (! [X5 : $i] : (((in @ X5 @ X1) = $true) => ((ap @ X2 @ X1 @ X4 @ (X0 @ X5)) = X5)) => ($true = (surjective @ X2 @ X1 @ X4)))))),
% 1.41/1.14 inference(fool_elimination,[status(thm)],[f5])).
% 1.41/1.14 thf(f5,plain,(
% 1.41/1.14 ~! [X0 : $i > $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X0 @ X3) @ X2)) => ! [X4 : $i] : ((in @ X4 @ (funcSet @ X2 @ X1)) => (! [X5 : $i] : ((in @ X5 @ X1) => ((ap @ X2 @ X1 @ X4 @ (X0 @ X5)) = X5)) => (surjective @ X2 @ X1 @ X4))))),
% 1.41/1.14 inference(rectify,[status(thm)],[f3])).
% 1.41/1.14 thf(f3,negated_conjecture,(
% 1.41/1.14 ~! [X2 : $i > $i,X0 : $i,X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X5 : $i] : ((in @ X5 @ (funcSet @ X1 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X1 @ X0 @ X5 @ (X2 @ X3)) = X3)) => (surjective @ X1 @ X0 @ X5))))),
% 1.41/1.14 inference(negated_conjecture,[status(cth)],[f2])).
% 1.41/1.14 thf(f2,conjecture,(
% 1.41/1.14 ! [X2 : $i > $i,X0 : $i,X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X5 : $i] : ((in @ X5 @ (funcSet @ X1 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X1 @ X0 @ X5 @ (X2 @ X3)) = X3)) => (surjective @ X1 @ X0 @ X5))))),
% 1.41/1.14 file('/export/starexec/sandbox/tmp/tmp.LY66uYPnul/DTF2THF_18143.p',leftInvIsSurj)).
% 1.41/1.14 thf(f36,plain,(
% 1.41/1.14 ( ! [X0 : $i] : (((in @ X0 @ sK1) != $true) | (sK5 != X0)) )),
% 1.41/1.14 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.41/1.14 thf(f35,plain,(
% 1.41/1.14 ( ! [X0 : $i] : (((in @ X0 @ sK1) != $true) | (sK5 != X0) | ($false = $true)) )),
% 1.41/1.14 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.41/1.14 thf(f32,plain,(
% 1.41/1.14 ( ! [X0 : $i] : (((in @ X0 @ sK1) != $true) | ($false = $true) | ((in @ X0 @ sK1) != $true) | (sK5 != X0)) )),
% 1.41/1.14 inference(superposition,[status(thm)],[f15,f30])).
% 1.41/1.14 thf(f30,plain,(
% 1.41/1.14 ( ! [X0 : $i] : (($false = (in @ (sK0 @ X0) @ sK2)) | (sK5 != X0) | ((in @ X0 @ sK1) != $true)) )),
% 1.41/1.14 inference(superposition,[status(thm)],[f29,f17])).
% 1.41/1.14 thf(f17,plain,(
% 1.41/1.14 ( ! [X4 : $i] : (((ap @ sK2 @ sK1 @ sK3 @ (sK0 @ X4)) = X4) | ((in @ X4 @ sK1) != $true)) )),
% 1.41/1.14 inference(cnf_transformation,[status(thm)],[f14])).
% 1.41/1.14 thf(f29,plain,(
% 1.41/1.14 ( ! [X1 : $i] : ((sK5 != (ap @ sK2 @ sK1 @ sK3 @ X1)) | ((in @ X1 @ sK2) = $false)) )),
% 1.41/1.14 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.41/1.14 thf(f28,plain,(
% 1.41/1.14 ( ! [X1 : $i] : (((in @ X1 @ sK2) = $false) | (((ap @ sK2 @ sK1 @ sK3 @ X1) = sK5) = $false)) )),
% 1.41/1.14 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.41/1.14 thf(f27,plain,(
% 1.41/1.14 ( ! [X1 : $i] : ((((in @ X1 @ sK2) & ((ap @ sK2 @ sK1 @ sK3 @ X1) = sK5)) = $false)) )),
% 1.41/1.14 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.41/1.14 thf(f26,plain,(
% 1.41/1.14 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((in @ Y0 @ sK2) & ((ap @ sK2 @ sK1 @ sK3 @ Y0) = sK5))) @ X1))) )),
% 1.41/1.14 inference(pi_clausification,[status(thm)],[f24])).
% 1.41/1.14 thf(f24,plain,(
% 1.41/1.14 ($false = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) & ((ap @ sK2 @ sK1 @ sK3 @ Y0) = sK5)))))),
% 1.41/1.14 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.41/1.14 thf(f15,plain,(
% 1.41/1.14 ( ! [X5 : $i] : (((in @ (sK0 @ X5) @ sK2) = $true) | ((in @ X5 @ sK1) != $true)) )),
% 1.41/1.14 inference(cnf_transformation,[status(thm)],[f14])).
% 1.41/1.14 % SZS output end Proof for DTF2THF_18143
% 1.41/1.14 % (18433)------------------------------
% 1.41/1.14 % (18433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.14 % (18433)Termination reason: Refutation
% 1.41/1.14
% 1.41/1.14 % (18433)Memory used [KB]: 5500
% 1.41/1.14 % (18433)Time elapsed: 0.007 s
% 1.41/1.14 % (18433)Instructions burned: 4 (million)
% 1.41/1.14 % (18433)------------------------------
% 1.41/1.14 % (18433)------------------------------
% 1.41/1.14 % (18432)Success in time 0.023 s
%------------------------------------------------------------------------------