%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO534^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:54:29 AM UTC 2026
% Result : Theorem 1.52s 1.30s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 358 ( 64 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 848 ( 10 ~; 15 |; 4 &; 687 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 93 ( 93 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 9 con; 0-3 aty)
% ( 0 !!; 126 ??; 0 @@+; 0 @@-)
% Number of variables : 234 ( 164 ^; 38 !; 32 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
epsa: ( $i > $i > $i > $o ) > $i ).
thf(func_def_3,type,
epsb: ( $i > $i > $i > $o ) > $i ).
thf(func_def_4,type,
epsc: ( $i > $i > $i > $o ) > $i ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
sK0: $i > $i > $i > $o ).
thf(func_def_18,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f53,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f27,f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( $false
= ( sK0 @ X1 @ X2 @ X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X2 @ X3 ) ) ),
inference(backward_demodulation,[status(thm)],[f45,f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1
@ X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1
@ X2 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[status(thm)],[f38,f46]) ).
thf(f46,plain,
! [X1: $i] :
( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) )
@ X1 ) ),
inference(subsumption_resolution,[status(thm)],[f35,f32]) ).
thf(f32,plain,
( $true
!= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) )
@ ( eps
@ ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
!= ( sK0
@ ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) )
@ sK0 )
@ ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( Y0
@ ( ^ [Y3: $i > $i > $i > $o] :
( eps
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] : ( Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ Y0 )
@ Y1
@ Y2 ) ) )
@ sK0 )
@ ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i > $i > $o] :
( eps
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] : ( Y2 @ Y3 @ Y4 @ Y5 ) ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $i > $i > $o] :
( eps
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( Y2
@ ( ^ [Y5: $i > $i > $i > $o] :
( eps
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] : ( Y5 @ Y6 @ Y7 @ Y8 ) ) ) )
@ Y2 )
@ Y3
@ Y4 ) ) )
@ Y0 )
@ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f26,f29,f30]) ).
thf(f30,plain,
( epsc
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i > $i > $o] :
( eps
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] : ( Y2 @ Y3 @ Y4 @ Y5 ) ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $i > $i > $o] :
( eps
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( Y2
@ ( ^ [Y5: $i > $i > $i > $o] :
( eps
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] : ( Y5 @ Y6 @ Y7 @ Y8 ) ) ) )
@ Y2 )
@ Y3
@ Y4 ) ) )
@ Y0 )
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f26,f29]) ).
thf(f23,plain,
( epsc
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( Y0 @ ( epsa @ Y0 ) @ ( epsb @ Y0 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( epsc
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( Y0 @ ( epsa @ Y0 ) @ ( epsb @ Y0 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( epsc
= ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] : ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( epsc
= ( ^ [X2: $i > $i > $i > $o] :
( eps
@ ^ [X4: $i] : ( X2 @ ( epsa @ X2 ) @ ( epsb @ X2 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2THF_15935.p',epscd) ).
thf(f29,plain,
( epsb
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( Y0
@ ( ^ [Y3: $i > $i > $i > $o] :
( eps
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] : ( Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ Y0 )
@ Y1
@ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f26]) ).
thf(f24,plain,
( epsb
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( epsb
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( epsb
= ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X2: $i] : ( X0 @ ( epsa @ X0 ) @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( epsb
= ( ^ [X2: $i > $i > $i > $o] :
( eps
@ ^ [X3: $i] :
? [X4: $i] : ( X2 @ ( epsa @ X2 ) @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2THF_15935.p',epsbd) ).
thf(f26,plain,
( epsa
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( epsa
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( epsa
= ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X2: $i,X3: $i] : ( X0 @ X1 @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( epsa
= ( ^ [X2: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X4: $i,X3: $i] : ( X2 @ X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2THF_15935.p',epsad) ).
thf(f28,plain,
( $true
!= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( epsc @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true
!= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( epsc @ sK0 ) ) )
& ( $true
= ( sK0 @ sK3 @ sK1 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f21,f20]) ).
thf(f20,plain,
( ? [X0: $i > $i > $i > $o] :
( ( $true
!= ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) ) )
& ? [X1: $i,X2: $i,X3: $i] :
( $true
= ( X0 @ X3 @ X1 @ X2 ) ) )
=> ( ( $true
!= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( epsc @ sK0 ) ) )
& ? [X3: $i,X2: $i,X1: $i] :
( $true
= ( sK0 @ X3 @ X1 @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X3: $i,X2: $i,X1: $i] :
( $true
= ( sK0 @ X3 @ X1 @ X2 ) )
=> ( $true
= ( sK0 @ sK3 @ sK1 @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
? [X0: $i > $i > $i > $o] :
( ( $true
!= ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) ) )
& ? [X1: $i,X2: $i,X3: $i] :
( $true
= ( X0 @ X3 @ X1 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $i > $i > $i > $o] :
( ? [X1: $i,X2: $i,X3: $i] :
( $true
= ( X0 @ X3 @ X1 @ X2 ) )
=> ( $true
= ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $i > $i > $i > $o] :
( ? [X1: $i,X2: $i,X3: $i] : ( X0 @ X3 @ X1 @ X2 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X2: $i > $i > $i > $o] :
( ? [X3: $i,X4: $i,X1: $i] : ( X2 @ X1 @ X3 @ X4 )
=> ( X2 @ ( epsa @ X2 ) @ ( epsb @ X2 ) @ ( epsc @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X2: $i > $i > $i > $o] :
( ? [X3: $i,X4: $i,X1: $i] : ( X2 @ X1 @ X3 @ X4 )
=> ( X2 @ ( epsa @ X2 ) @ ( epsb @ X2 ) @ ( epsc @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2THF_15935.p',conj) ).
thf(f35,plain,
! [X1: $i] :
( ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) )
@ X1 ) )
| ( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) )
@ ( eps
@ ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) )
@ sK5 ) )
| ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1
@ X2 ) ) ),
inference(sigma_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1
@ X2 ) )
| ( $true
= ( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) )
= $false )
| ( $true
= ( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) )
@ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK6
@ sK7 ) )
| ( $false
= ( sK0 @ X1 @ X2 @ X3 ) ) ),
inference(sigma_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK6 ) ) )
| ( $false
= ( sK0 @ X1 @ X2 @ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( ( ?? @ $i @ ( sK0 @ X1 @ X2 ) )
= $false )
| ( $true
= ( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( ( ?? @ $i @ ( sK0 @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) )
@ sK6 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) )
| ( ( ?? @ $i @ ( sK0 @ X1 @ X2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ X1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ( sK0
@ ( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( ?? @ $i @ ( sK0 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) )
@ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) )
@ ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( ?? @ $i @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( $true
= ( sK0 @ sK3 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO534^1 : TPTP v9.2.1. Released v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n019.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 14:33:24 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SYO534^1 : TPTP v9.2.1. Released v5.2.0.
% 0.16/0.42 % Domain : Syntactic
% 0.16/0.42 % Problem : 3-ary choice on individuals
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English : epsa, epsb and epsc work together to give an a, b and c such that
% 0.16/0.42 % R a b c holds, if such an a, b and c exist for a 3-ary relation R
% 0.16/0.42 % on $i. A choice operator on i can be used to define a choice
% 0.16/0.42 % operator on i*i*i (Curried). In this version, the solution is
% 0.16/0.42 % given and the goal is to check that it works.
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro11]
% 0.16/0.42 % Names : CHOICE11 [Bro11]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.11 v9.1.0, 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.22 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, 0.43 v6.1.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0
% 0.16/0.42 % Syntax : Number of formulae : 9 ( 3 unt; 4 typ; 3 def)
% 0.16/0.42 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 1 ( 0 avg)
% 0.16/0.42 % Number of connectives : 29 ( 0 ~; 0 |; 0 &; 27 @)
% 0.16/0.42 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 9 ( 3 avg)
% 0.16/0.42 % Number of types : 2 ( 0 usr)
% 0.16/0.42 % Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.16/0.42 % Number of variables : 15 ( 6 ^; 2 !; 7 ?; 15 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments :
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(eps,type,
% 0.16/0.42 eps: ( $i > $o ) > $i ).
% 0.16/0.42
% 0.16/0.42 thf(choiceax,axiom,
% 0.16/0.42 ! [P: $i > $o] :
% 0.16/0.42 ( ? [X: $i] : ( P @ X )
% 0.16/0.42 => ( P @ ( eps @ P ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(epsa,type,
% 0.16/0.42 epsa: ( $i > $i > $i > $o ) > $i ).
% 0.16/0.42
% 0.16/0.42 thf(epsad,definition,
% 0.16/0.42 ( epsa
% 0.16/0.42 = ( ^ [R: $i > $i > $i > $o] :
% 0.16/0.42 ( eps
% 0.16/0.42 @ ^ [X: $i] :
% 0.16/0.42 ? [Y: $i,Z: $i] : ( R @ X @ Y @ Z ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(epsb,type,
% 0.16/0.42 epsb: ( $i > $i > $i > $o ) > $i ).
% 0.16/0.42
% 0.16/0.42 thf(epsbd,definition,
% 0.16/0.42 ( epsb
% 0.16/0.42 = ( ^ [R: $i > $i > $i > $o] :
% 0.16/0.42 ( eps
% 0.16/0.42 @ ^ [Y: $i] :
% 0.16/0.42 ? [Z: $i] : ( R @ ( epsa @ R ) @ Y @ Z ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(epsc,type,
% 0.16/0.42 epsc: ( $i > $i > $i > $o ) > $i ).
% 0.16/0.42
% 0.16/0.42 thf(epscd,definition,
% 0.16/0.42 ( epsc
% 0.16/0.42 = ( ^ [R: $i > $i > $i > $o] :
% 0.16/0.42 ( eps
% 0.16/0.42 @ ^ [Z: $i] : ( R @ ( epsa @ R ) @ ( epsb @ R ) @ Z ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(conj,conjecture,
% 0.16/0.42 ! [R: $i > $i > $i > $o] :
% 0.16/0.42 ( ? [X: $i,Y: $i,Z: $i] : ( R @ X @ Y @ Z )
% 0.16/0.42 => ( R @ ( epsa @ R ) @ ( epsb @ R ) @ ( epsc @ R ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.46/1.22 ---- Embedded in THF ---
% 1.46/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.22 %%% Generated on Tue Feb 24 14:33:25 EST 2026
% 1.46/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.22 %%% Logic specification used:
% 1.46/1.22 %%% thf(spec, logic, $$dhol).
% 1.46/1.22
% 1.46/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2DTF15935.p
% See solution above
% 1.46/1.22 ------------------------
% 1.46/1.23 ---- Cleaned THF ---
% 1.46/1.23 thf(eps,type,
% 1.46/1.23 eps: ( $i > $o ) > $i ).
% 1.46/1.23
% 1.46/1.23 thf(choiceax,axiom,
% 1.46/1.23 ! [P: $i > $o] :
% 1.46/1.23 ( ? [X: $i] : ( P @ X )
% 1.46/1.23 => ( P @ ( eps @ P ) ) ) ).
% 1.46/1.23
% 1.46/1.23 thf(epsa,type,
% 1.46/1.23 epsa: ( $i > $i > $i > $o ) > $i ).
% 1.46/1.23
% 1.46/1.23 thf(epsad,definition,
% 1.46/1.23 ( epsa
% 1.46/1.23 = ( ^ [R: $i > $i > $i > $o] :
% 1.46/1.23 ( eps
% 1.46/1.23 @ ^ [X: $i] :
% 1.46/1.23 ? [Y: $i,Z: $i] : ( R @ X @ Y @ Z ) ) ) ) ).
% 1.46/1.23
% 1.46/1.23 thf(epsb,type,
% 1.46/1.23 epsb: ( $i > $i > $i > $o ) > $i ).
% 1.46/1.23
% 1.46/1.23 thf(epsbd,definition,
% 1.46/1.23 ( epsb
% 1.46/1.23 = ( ^ [R: $i > $i > $i > $o] :
% 1.46/1.23 ( eps
% 1.46/1.23 @ ^ [Y: $i] :
% 1.46/1.23 ? [Z: $i] : ( R @ ( epsa @ R ) @ Y @ Z ) ) ) ) ).
% 1.46/1.23
% 1.46/1.23 thf(epsc,type,
% 1.46/1.23 epsc: ( $i > $i > $i > $o ) > $i ).
% 1.46/1.23
% 1.46/1.23 thf(epscd,definition,
% 1.46/1.23 ( epsc
% 1.46/1.23 = ( ^ [R: $i > $i > $i > $o] :
% 1.46/1.23 ( eps
% 1.46/1.23 @ ^ [Z: $i] : ( R @ ( epsa @ R ) @ ( epsb @ R ) @ Z ) ) ) ) ).
% 1.46/1.23
% 1.46/1.23 thf(conj,conjecture,
% 1.46/1.23 ! [R: $i > $i > $i > $o] :
% 1.46/1.23 ( ? [X: $i,Y: $i,Z: $i] : ( R @ X @ Y @ Z )
% 1.46/1.23 => ( R @ ( epsa @ R ) @ ( epsb @ R ) @ ( epsc @ R ) ) ) ).
% 1.46/1.23 ------------------------
% 1.46/1.25 % (16033)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/183Mi)
% 1.46/1.25 % (16039)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/18Mi)
% 1.46/1.25 % (16037)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_15935 for (2999ds/2Mi)
% 1.46/1.25 % (16036)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/2Mi)
% 1.46/1.25 % (16034)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_15935 for (2999ds/4Mi)
% 1.46/1.26 % (16037)Instruction limit reached!
% 1.46/1.26 % (16037)------------------------------
% 1.46/1.26 % (16037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (16037)Termination reason: Unknown
% 1.46/1.26 % (16037)Termination phase: Property scanning
% 1.46/1.26
% 1.46/1.26 % (16037)Memory used [KB]: 1023
% 1.46/1.26 % (16037)Time elapsed: 0.003 s
% 1.46/1.26 % (16037)Instructions burned: 3 (million)
% 1.46/1.26 % (16037)------------------------------
% 1.46/1.26 % (16037)------------------------------
% 1.46/1.26 % (16038)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_15935 for (2999ds/275Mi)
% 1.46/1.26 % (16035)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_15935 for (2999ds/27Mi)
% 1.46/1.26 % (16036)Instruction limit reached!
% 1.46/1.26 % (16036)------------------------------
% 1.46/1.26 % (16036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (16036)Termination reason: Unknown
% 1.46/1.26 % (16036)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (16036)Memory used [KB]: 1023
% 1.46/1.26 % (16036)Time elapsed: 0.003 s
% 1.46/1.26 % (16036)Instructions burned: 3 (million)
% 1.46/1.26 % (16036)------------------------------
% 1.46/1.26 % (16036)------------------------------
% 1.46/1.26 % (16034)Instruction limit reached!
% 1.46/1.26 % (16034)------------------------------
% 1.46/1.26 % (16034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (16034)Termination reason: Unknown
% 1.46/1.26 % (16034)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (16034)Memory used [KB]: 5500
% 1.46/1.26 % (16034)Time elapsed: 0.004 s
% 1.46/1.26 % (16034)Instructions burned: 4 (million)
% 1.46/1.26 % (16034)------------------------------
% 1.46/1.26 % (16034)------------------------------
% 1.46/1.26 % (16038)Refutation not found, incomplete strategy
% 1.46/1.26 % (16038)------------------------------
% 1.46/1.26 % (16038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (16038)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.26
% 1.46/1.26
% 1.46/1.26 % (16038)Memory used [KB]: 5500
% 1.46/1.26 % (16038)Time elapsed: 0.004 s
% 1.46/1.26 % (16038)Instructions burned: 3 (million)
% 1.46/1.26 % (16038)------------------------------
% 1.46/1.26 % (16038)------------------------------
% 1.46/1.26 % (16039)Instruction limit reached!
% 1.46/1.26 % (16039)------------------------------
% 1.46/1.26 % (16039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (16039)Termination reason: Unknown
% 1.46/1.26 % (16039)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (16039)Memory used [KB]: 5628
% 1.46/1.26 % (16039)Time elapsed: 0.013 s
% 1.46/1.26 % (16039)Instructions burned: 19 (million)
% 1.46/1.26 % (16039)------------------------------
% 1.46/1.26 % (16039)------------------------------
% 1.46/1.27 % (16035)Instruction limit reached!
% 1.46/1.27 % (16035)------------------------------
% 1.46/1.27 % (16035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (16035)Termination reason: Unknown
% 1.46/1.27 % (16035)Termination phase: Saturation
% 1.46/1.27
% 1.46/1.27 % (16035)Memory used [KB]: 5756
% 1.46/1.27 % (16040)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/3Mi)
% 1.46/1.27 % (16035)Time elapsed: 0.019 s
% 1.46/1.27 % (16035)Instructions burned: 28 (million)
% 1.46/1.27 % (16035)------------------------------
% 1.46/1.27 % (16035)------------------------------
% 1.46/1.27 % (16042)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/15Mi)
% 1.46/1.27 % (16040)Instruction limit reached!
% 1.46/1.27 % (16040)------------------------------
% 1.46/1.27 % (16040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (16040)Termination reason: Unknown
% 1.46/1.27 % (16040)Termination phase: Saturation
% 1.46/1.27
% 1.46/1.28 % (16040)Memory used [KB]: 5500
% 1.46/1.28 % (16040)Time elapsed: 0.004 s
% 1.46/1.28 % (16040)Instructions burned: 4 (million)
% 1.46/1.28 % (16040)------------------------------
% 1.46/1.28 % (16040)------------------------------
% 1.46/1.28 % (16041)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_15935 for (2999ds/37Mi)
% 1.46/1.28 % (16043)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/3Mi)
% 1.46/1.28 % (16043)Instruction limit reached!
% 1.46/1.28 % (16043)------------------------------
% 1.46/1.28 % (16043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (16043)Termination reason: Unknown
% 1.46/1.28 % (16043)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (16043)Memory used [KB]: 5500
% 1.46/1.28 % (16043)Time elapsed: 0.004 s
% 1.46/1.28 % (16043)Instructions burned: 3 (million)
% 1.46/1.28 % (16043)------------------------------
% 1.46/1.28 % (16043)------------------------------
% 1.46/1.28 % (16044)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/1041Mi)
% 1.46/1.28 % (16042)Refutation not found, incomplete strategy
% 1.46/1.28 % (16042)------------------------------
% 1.46/1.28 % (16042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (16042)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.28
% 1.46/1.28
% 1.46/1.28 % (16042)Memory used [KB]: 5628
% 1.46/1.28 % (16042)Time elapsed: 0.009 s
% 1.46/1.28 % (16042)Instructions burned: 13 (million)
% 1.46/1.28 % (16042)------------------------------
% 1.46/1.28 % (16042)------------------------------
% 1.46/1.29 % (16045)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/7Mi)
% 1.46/1.29 % (16046)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/16Mi)
% 1.46/1.30 % (16041)Instruction limit reached!
% 1.46/1.30 % (16041)------------------------------
% 1.46/1.30 % (16041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (16041)Termination reason: Unknown
% 1.46/1.30 % (16041)Termination phase: Saturation
% 1.46/1.30
% 1.46/1.30 % (16041)Memory used [KB]: 5884
% 1.46/1.30 % (16041)Time elapsed: 0.022 s
% 1.46/1.30 % (16041)Instructions burned: 38 (million)
% 1.46/1.30 % (16041)------------------------------
% 1.46/1.30 % (16041)------------------------------
% 1.52/1.30 % (16045)First to succeed.
% 1.52/1.30 % (16033)Instruction limit reached!
% 1.52/1.30 % (16033)------------------------------
% 1.52/1.30 % (16033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (16033)Termination reason: Unknown
% 1.52/1.30 % (16033)Termination phase: Saturation
% 1.52/1.30
% 1.52/1.30 % (16033)Memory used [KB]: 6268
% 1.52/1.30 % (16033)Time elapsed: 0.055 s
% 1.52/1.30 % (16033)Instructions burned: 184 (million)
% 1.52/1.30 % (16033)------------------------------
% 1.52/1.30 % (16033)------------------------------
% 1.52/1.30 % (16047)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_15935 for (2999ds/3Mi)
% 1.52/1.30 % (16045)Refutation found. Thanks to Tanya!
% 1.52/1.30 % SZS status Theorem for DTF2THF_15935
% 1.52/1.30 % SZS output start Proof for DTF2THF_15935
% 1.52/1.30 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.52/1.30 thf(func_def_2, type, epsa: ($i > $i > $i > $o) > $i).
% 1.52/1.30 thf(func_def_3, type, epsb: ($i > $i > $i > $o) > $i).
% 1.52/1.30 thf(func_def_4, type, epsc: ($i > $i > $i > $o) > $i).
% 1.52/1.30 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.52/1.30 thf(func_def_14, type, sK0: $i > $i > $i > $o).
% 1.52/1.30 thf(func_def_18, type, ph4: !>[X0: $tType]:(X0)).
% 1.52/1.30 thf(f53,plain,(
% 1.52/1.30 $false),
% 1.52/1.30 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.52/1.30 thf(f52,plain,(
% 1.52/1.30 ($true = $false)),
% 1.52/1.30 inference(backward_demodulation,[status(thm)],[f27,f51])).
% 1.52/1.30 thf(f51,plain,(
% 1.52/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (sK0 @ X1 @ X2 @ X3))) )),
% 1.52/1.30 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.52/1.30 thf(f50,plain,(
% 1.52/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ($false = (sK0 @ X1 @ X2 @ X3))) )),
% 1.52/1.30 inference(backward_demodulation,[status(thm)],[f45,f49])).
% 1.52/1.30 thf(f49,plain,(
% 1.52/1.30 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ X1 @ X2))) )),
% 1.52/1.30 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.52/1.30 thf(f48,plain,(
% 1.52/1.30 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ X1 @ X2)) | ($true = $false)) )),
% 1.52/1.30 inference(forward_demodulation,[status(thm)],[f38,f46])).
% 1.52/1.30 thf(f46,plain,(
% 1.52/1.30 ( ! [X1 : $i] : (($false = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0)))) @ X1))) )),
% 1.52/1.30 inference(subsumption_resolution,[status(thm)],[f35,f32])).
% 1.52/1.30 thf(f32,plain,(
% 1.52/1.30 ($true != (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0)))) @ (eps @ (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0))))))))),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.52/1.30 thf(f31,plain,(
% 1.52/1.30 ($true != (sK0 @ ((^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (Y0 @ Y1 @ Y2 @ Y3)))))))) @ sK0) @ ((^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ ((^[Y3 : $i > $i > $i > $o]: (eps @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (Y3 @ Y4 @ Y5 @ Y6)))))))) @ Y0) @ Y1 @ Y2)))))) @ sK0) @ ((^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $i > $o]: (eps @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (Y2 @ Y3 @ Y4 @ Y5)))))))) @ Y0) @ ((^[Y2 : $i > $i > $i > $o]: (eps @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ ((^[Y5 : $i > $i > $i > $o]: (eps @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (Y5 @ Y6 @ Y7 @ Y8)))))))) @ Y2) @ Y3 @ Y4)))))) @ Y0) @ Y1)))) @ sK0)))),
% 1.52/1.30 inference(definition_unfolding,[status(thm)],[f28,f26,f29,f30])).
% 1.52/1.30 thf(f30,plain,(
% 1.52/1.30 (epsc = (^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $i > $o]: (eps @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (Y2 @ Y3 @ Y4 @ Y5)))))))) @ Y0) @ ((^[Y2 : $i > $i > $i > $o]: (eps @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ ((^[Y5 : $i > $i > $i > $o]: (eps @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (Y5 @ Y6 @ Y7 @ Y8)))))))) @ Y2) @ Y3 @ Y4)))))) @ Y0) @ Y1)))))),
% 1.52/1.30 inference(definition_unfolding,[status(thm)],[f23,f26,f29])).
% 1.52/1.30 thf(f23,plain,(
% 1.52/1.30 (epsc = (^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ (epsa @ Y0) @ (epsb @ Y0) @ Y1)))))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.30 thf(f17,plain,(
% 1.52/1.30 (epsc = (^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ (epsa @ Y0) @ (epsb @ Y0) @ Y1)))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f16])).
% 1.52/1.30 thf(f16,plain,(
% 1.52/1.30 (epsc = (^[X0 : $i > $i > $i > $o] : (eps @ (^[X1 : $i] : (X0 @ (epsa @ X0) @ (epsb @ X0) @ X1)))))),
% 1.52/1.30 inference(rectify,[status(thm)],[f4])).
% 1.52/1.30 thf(f4,axiom,(
% 1.52/1.30 (epsc = (^[X2 : $i > $i > $i > $o] : (eps @ (^[X4 : $i] : (X2 @ (epsa @ X2) @ (epsb @ X2) @ X4)))))),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2THF_15935.p',epscd)).
% 1.52/1.30 thf(f29,plain,(
% 1.52/1.30 (epsb = (^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ ((^[Y3 : $i > $i > $i > $o]: (eps @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (Y3 @ Y4 @ Y5 @ Y6)))))))) @ Y0) @ Y1 @ Y2)))))))),
% 1.52/1.30 inference(definition_unfolding,[status(thm)],[f24,f26])).
% 1.52/1.30 thf(f24,plain,(
% 1.52/1.30 (epsb = (^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ (epsa @ Y0) @ Y1 @ Y2)))))))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.52/1.30 thf(f15,plain,(
% 1.52/1.30 (epsb = (^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ (epsa @ Y0) @ Y1 @ Y2)))))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f14])).
% 1.52/1.30 thf(f14,plain,(
% 1.52/1.30 (epsb = (^[X0 : $i > $i > $i > $o] : (eps @ (^[X1 : $i] : (? [X2 : $i] : (X0 @ (epsa @ X0) @ X1 @ X2))))))),
% 1.52/1.30 inference(rectify,[status(thm)],[f3])).
% 1.52/1.30 thf(f3,axiom,(
% 1.52/1.30 (epsb = (^[X2 : $i > $i > $i > $o] : (eps @ (^[X3 : $i] : (? [X4 : $i] : (X2 @ (epsa @ X2) @ X3 @ X4))))))),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2THF_15935.p',epsbd)).
% 1.52/1.30 thf(f26,plain,(
% 1.52/1.30 (epsa = (^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (Y0 @ Y1 @ Y2 @ Y3)))))))))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f9])).
% 1.52/1.30 thf(f9,plain,(
% 1.52/1.30 (epsa = (^[Y0 : $i > $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (Y0 @ Y1 @ Y2 @ Y3)))))))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f8])).
% 1.52/1.30 thf(f8,plain,(
% 1.52/1.30 (epsa = (^[X0 : $i > $i > $i > $o] : (eps @ (^[X1 : $i] : (? [X2 : $i,X3 : $i] : (X0 @ X1 @ X3 @ X2))))))),
% 1.52/1.30 inference(rectify,[status(thm)],[f2])).
% 1.52/1.30 thf(f2,axiom,(
% 1.52/1.30 (epsa = (^[X2 : $i > $i > $i > $o] : (eps @ (^[X1 : $i] : (? [X4 : $i,X3 : $i] : (X2 @ X1 @ X3 @ X4))))))),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2THF_15935.p',epsad)).
% 1.52/1.30 thf(f28,plain,(
% 1.52/1.30 ($true != (sK0 @ (epsa @ sK0) @ (epsb @ sK0) @ (epsc @ sK0)))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f22])).
% 1.52/1.30 thf(f22,plain,(
% 1.52/1.30 ($true != (sK0 @ (epsa @ sK0) @ (epsb @ sK0) @ (epsc @ sK0))) & ($true = (sK0 @ sK3 @ sK1 @ sK2))),
% 1.52/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f21,f20])).
% 1.52/1.30 thf(f20,plain,(
% 1.52/1.30 ? [X0 : $i > $i > $i > $o] : (($true != (X0 @ (epsa @ X0) @ (epsb @ X0) @ (epsc @ X0))) & ? [X1 : $i,X2 : $i,X3 : $i] : ($true = (X0 @ X3 @ X1 @ X2))) => (($true != (sK0 @ (epsa @ sK0) @ (epsb @ sK0) @ (epsc @ sK0))) & ? [X3 : $i,X2 : $i,X1 : $i] : ($true = (sK0 @ X3 @ X1 @ X2)))),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f21,plain,(
% 1.52/1.30 ? [X3 : $i,X2 : $i,X1 : $i] : ($true = (sK0 @ X3 @ X1 @ X2)) => ($true = (sK0 @ sK3 @ sK1 @ sK2))),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f18,plain,(
% 1.52/1.30 ? [X0 : $i > $i > $i > $o] : (($true != (X0 @ (epsa @ X0) @ (epsb @ X0) @ (epsc @ X0))) & ? [X1 : $i,X2 : $i,X3 : $i] : ($true = (X0 @ X3 @ X1 @ X2)))),
% 1.52/1.30 inference(ennf_transformation,[status(thm)],[f11])).
% 1.52/1.30 thf(f11,plain,(
% 1.52/1.30 ~! [X0 : $i > $i > $i > $o] : (? [X1 : $i,X2 : $i,X3 : $i] : ($true = (X0 @ X3 @ X1 @ X2)) => ($true = (X0 @ (epsa @ X0) @ (epsb @ X0) @ (epsc @ X0))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f10])).
% 1.52/1.30 thf(f10,plain,(
% 1.52/1.30 ~! [X0 : $i > $i > $i > $o] : (? [X1 : $i,X2 : $i,X3 : $i] : (X0 @ X3 @ X1 @ X2) => (X0 @ (epsa @ X0) @ (epsb @ X0) @ (epsc @ X0)))),
% 1.52/1.30 inference(rectify,[status(thm)],[f6])).
% 1.52/1.30 thf(f6,negated_conjecture,(
% 1.52/1.30 ~! [X2 : $i > $i > $i > $o] : (? [X3 : $i,X4 : $i,X1 : $i] : (X2 @ X1 @ X3 @ X4) => (X2 @ (epsa @ X2) @ (epsb @ X2) @ (epsc @ X2)))),
% 1.52/1.30 inference(negated_conjecture,[status(cth)],[f5])).
% 1.52/1.30 thf(f5,conjecture,(
% 1.52/1.30 ! [X2 : $i > $i > $i > $o] : (? [X3 : $i,X4 : $i,X1 : $i] : (X2 @ X1 @ X3 @ X4) => (X2 @ (epsa @ X2) @ (epsb @ X2) @ (epsc @ X2)))),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.HhJ6QMvoWy/DTF2THF_15935.p',conj)).
% 1.52/1.30 thf(f35,plain,(
% 1.52/1.30 ( ! [X1 : $i] : (($false = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0)))) @ X1)) | ($true = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0)))) @ (eps @ (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0))))))))) )),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f38,plain,(
% 1.52/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0)))) @ sK5)) | ($false = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ X1 @ X2))) )),
% 1.52/1.30 inference(sigma_clausification,[status(thm)],[f37])).
% 1.52/1.30 thf(f37,plain,(
% 1.52/1.30 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ X1 @ X2)) | ($true = (?? @ $i @ (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0)))))))) )),
% 1.52/1.30 inference(pi_clausification,[status(thm)],[f36])).
% 1.52/1.30 thf(f36,plain,(
% 1.52/1.30 ( ! [X1 : $i] : (((?? @ $i @ (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ X1)) = $false) | ($true = (?? @ $i @ (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0)))))))) )),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.52/1.30 thf(f34,plain,(
% 1.52/1.30 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0))) @ X1) = $false) | ($true = ((^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0))))))) )),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f45,plain,(
% 1.52/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ sK6 @ sK7)) | ($false = (sK0 @ X1 @ X2 @ X3))) )),
% 1.52/1.30 inference(sigma_clausification,[status(thm)],[f44])).
% 1.52/1.30 thf(f44,plain,(
% 1.52/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (?? @ $i @ (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ sK6))) | ($false = (sK0 @ X1 @ X2 @ X3))) )),
% 1.52/1.30 inference(pi_clausification,[status(thm)],[f43])).
% 1.52/1.30 thf(f43,plain,(
% 1.52/1.30 ( ! [X2 : $i,X1 : $i] : (((?? @ $i @ (sK0 @ X1 @ X2)) = $false) | ($true = (?? @ $i @ (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1)))))) @ sK6)))) )),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.52/1.30 thf(f42,plain,(
% 1.52/1.30 ( ! [X2 : $i,X1 : $i] : (((?? @ $i @ (sK0 @ X1 @ X2)) = $false) | (((^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0))) @ sK6) = $true)) )),
% 1.52/1.30 inference(sigma_clausification,[status(thm)],[f41])).
% 1.52/1.30 thf(f41,plain,(
% 1.52/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0))))) | ((?? @ $i @ (sK0 @ X1 @ X2)) = $false)) )),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.52/1.30 thf(f40,plain,(
% 1.52/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0))))) | ($false = ((^[Y0 : $i]: (?? @ $i @ (sK0 @ X1 @ Y0))) @ X2))) )),
% 1.52/1.30 inference(pi_clausification,[status(thm)],[f39])).
% 1.52/1.30 thf(f39,plain,(
% 1.52/1.30 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ X1 @ Y0))))) | ($true = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (sK0 @ Y1 @ Y2)))))) @ Y0)))))) )),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.52/1.30 thf(f33,plain,(
% 1.52/1.30 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1))))) @ X1) = $false) | ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1))))) @ (eps @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (sK0 @ Y0 @ Y1))))))))) )),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f27,plain,(
% 1.52/1.30 ($true = (sK0 @ sK3 @ sK1 @ sK2))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f22])).
% 1.52/1.30 % SZS output end Proof for DTF2THF_15935
% 1.52/1.30 % (16045)------------------------------
% 1.52/1.30 % (16045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (16045)Termination reason: Refutation
% 1.52/1.30
% 1.52/1.30 % (16045)Memory used [KB]: 1023
% 1.52/1.30 % (16045)Time elapsed: 0.008 s
% 1.52/1.30 % (16045)Instructions burned: 5 (million)
% 1.52/1.30 % (16045)------------------------------
% 1.52/1.30 % (16045)------------------------------
% 1.52/1.30 % (16032)Success in time 0.056 s
%------------------------------------------------------------------------------