%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU699^2 : 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 : n018.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 09:36:29 AM UTC 2026
% Result : Theorem 1.81s 1.54s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 5
% Syntax : Number of formulae : 93 ( 90 unt; 0 typ; 0 def)
% Number of atoms : 1107 ( 185 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 2550 ( 8 ~; 0 |; 0 &;2018 @)
% ( 0 <=>; 271 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 11 con; 0-4 aty)
% ( 253 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 384 ( 287 ^; 97 !; 0 ?; 384 :)
% 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_5,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_22,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f177,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f174,f165]) ).
thf(f165,plain,
( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ sK5 )
!= ( ap @ sK4 @ sK3 @ sK2 @ sK5 ) ),
inference(equality_proxy_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
( $false
= ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ sK5 )
= ( ap @ sK4 @ sK3 @ sK2 @ sK5 ) ) ),
inference(boolean_simplification,[status(thm)],[f157]) ).
thf(f157,plain,
( $false
= ( $true
=> ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ sK5 )
= ( ap @ sK4 @ sK3 @ sK2 @ sK5 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f154,f156]) ).
thf(f156,plain,
( ( in @ sK5 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
( $false
= ( ( in @ sK5 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ sK5 )
= ( ap @ sK4 @ sK3 @ sK2 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f150]) ).
thf(f150,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f143]) ).
thf(f143,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) ) ) )
=> $false ) ),
inference(forward_demodulation,[status(thm)],[f142,f73]) ).
thf(f73,plain,
( $false
= ( sK2
= ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
= ( $true
=> ( sK2
= ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f69,f71]) ).
thf(f71,plain,
( ( in @ sK2 @ ( funcSet @ sK4 @ sK3 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( in @ sK2 @ ( funcSet @ sK4 @ sK3 ) )
=> ( sK2
= ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ^ [Y0: $i] :
( ( in @ sK2 @ ( funcSet @ Y0 @ sK3 ) )
=> ( sK2
= ( lam @ Y0 @ sK3 @ ( ap @ Y0 @ sK3 @ sK2 ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ sK2 @ ( funcSet @ Y0 @ sK3 ) )
=> ( sK2
= ( lam @ Y0 @ sK3 @ ( ap @ Y0 @ sK3 @ sK2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ sK2 @ ( funcSet @ Y1 @ Y0 ) )
=> ( sK2
= ( lam @ Y1 @ Y0 @ ( ap @ Y1 @ Y0 @ sK2 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ sK2 @ ( funcSet @ Y1 @ Y0 ) )
=> ( sK2
= ( lam @ Y1 @ Y0 @ ( ap @ Y1 @ Y0 @ sK2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1 @ ( ap @ Y2 @ Y1 @ Y0 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1 @ ( ap @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ ( lam @ Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1 @ ( ap @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ ( lam @ Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1 @ ( ap @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f41,f55]) ).
thf(f55,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ ( lam @ Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1 @ ( ap @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y1 @ Y3 ) @ Y0 ) ) )
=> ( in @ ( lam @ Y2 @ Y0 @ Y1 ) @ ( funcSet @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ ( lam @ Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1 @ ( ap @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y0 @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y1 @ Y3 ) @ Y0 ) ) )
=> ( in @ ( lam @ Y2 @ Y0 @ Y1 ) @ ( funcSet @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ ( lam @ Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1 @ ( ap @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y0 @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y1 @ Y3 ) @ Y0 ) ) )
=> ( in @ ( lam @ Y2 @ Y0 @ Y1 ) @ ( funcSet @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ ( lam @ Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1 @ ( ap @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y0 @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y1 @ Y3 ) @ Y0 ) ) )
=> ( in
@ ( lam @ Y2 @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) )
@ ( funcSet @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1
@ ( lam @ Y0 @ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1
@ ^ [Y3: $i] : ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f20,f19,f22,f18]) ).
thf(f18,plain,
( beta2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1
@ ( lam @ Y0 @ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( beta2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1
@ ( lam @ Y0 @ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( beta2
= ( ! [X0: $i > $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( X0 @ X3 ) @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X0 @ X4 )
= ( ap @ X2 @ X1
@ ( lam @ X2 @ X1
@ ^ [X5: $i] : ( X0 @ X5 ) )
@ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( beta2
= ( ! [X2: $i > $i,X1: $i,X0: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 @ X3 )
= ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X5: $i] : ( X2 @ X5 ) )
@ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',beta2) ).
thf(f22,plain,
( funcext2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( funcext2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( funcext2
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X2 @ X0 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ap @ X2 @ X0 @ X3 @ X4 )
= ( ap @ X2 @ X0 @ X1 @ X4 ) ) )
=> ( X1 = X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( funcext2
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X4 @ X3 ) ) )
=> ( X2 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',funcext2) ).
thf(f19,plain,
( lam2p
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y1 @ Y3 ) @ Y0 ) ) )
=> ( in
@ ( lam @ Y2 @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) )
@ ( funcSet @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( lam2p
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y1 @ Y3 ) @ Y0 ) ) )
=> ( in
@ ( lam @ Y2 @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) )
@ ( funcSet @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( lam2p
= ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X1 @ X3 ) @ X2 ) )
=> ( in
@ ( lam @ X0 @ X2
@ ^ [X4: $i] : ( X1 @ X4 ) )
@ ( funcSet @ X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( lam2p
= ( ! [X0: $i,X2: $i > $i,X1: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( in
@ ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
@ ( funcSet @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',lam2p) ).
thf(f20,plain,
( ap2p
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y0 @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ap2p
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y0 @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ap2p
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X2 @ X1 @ X3 ) @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ap2p
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',ap2p) ).
thf(f21,plain,
( ( ~ ( ap2p
=> ( lam2p
=> ( funcext2
=> ( beta2
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1
@ ^ [Y3: $i] : ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ~ ( ap2p
=> ( lam2p
=> ( funcext2
=> ( beta2
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( Y0
= ( lam @ Y2 @ Y1
@ ^ [Y3: $i] : ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ap2p
=> ( lam2p
=> ( funcext2
=> ( beta2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( X2
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ap2p
=> ( lam2p
=> ( funcext2
=> ( beta2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( X2
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ap2p
=> ( lam2p
=> ( funcext2
=> ( beta2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( X2
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',eta2) ).
thf(f142,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) ) ) )
=> ( sK2
= ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f136]) ).
thf(f136,plain,
( $true
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) ) ) )
=> ( sK2
= ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f131,f84]) ).
thf(f84,plain,
( $true
= ( in @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ ( funcSet @ sK4 @ sK3 ) ) ),
inference(boolean_simplification,[status(thm)],[f81]) ).
thf(f81,plain,
( $true
= ( $true
=> ( in @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ ( funcSet @ sK4 @ sK3 ) ) ) ),
inference(superposition,[status(thm)],[f52,f75]) ).
thf(f75,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( in @ ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) @ sK3 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f74]) ).
thf(f74,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( in @ ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) @ sK3 ) ) ) ) ),
inference(superposition,[status(thm)],[f39,f71]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( ap @ X3 @ X1 @ X2 @ Y0 ) @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( funcSet @ Y0 @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( ap @ Y0 @ X1 @ X2 @ Y1 ) @ X1 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( funcSet @ Y0 @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( ap @ Y0 @ X1 @ X2 @ Y1 ) @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( funcSet @ Y1 @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( ap @ Y1 @ X1 @ Y0 @ Y2 ) @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( funcSet @ Y1 @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( ap @ Y1 @ X1 @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y0 @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y0 @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f52,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( X2 @ Y0 ) @ X1 ) ) )
=> ( in @ ( lam @ X3 @ X1 @ X2 ) @ ( funcSet @ X3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( X2 @ Y1 ) @ X1 ) ) )
=> ( in @ ( lam @ Y0 @ X1 @ X2 ) @ ( funcSet @ Y0 @ X1 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i > $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( X2 @ Y1 ) @ X1 ) ) )
=> ( in @ ( lam @ Y0 @ X1 @ X2 ) @ ( funcSet @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i > $i,X1: $i] :
( $true
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( Y0 @ Y2 ) @ X1 ) ) )
=> ( in @ ( lam @ Y1 @ X1 @ Y0 ) @ ( funcSet @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( Y0 @ Y2 ) @ X1 ) ) )
=> ( in @ ( lam @ Y1 @ X1 @ Y0 ) @ ( funcSet @ Y1 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y1 @ Y3 ) @ Y0 ) ) )
=> ( in @ ( lam @ Y2 @ Y0 @ Y1 ) @ ( funcSet @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y1 @ Y3 ) @ Y0 ) ) )
=> ( in @ ( lam @ Y2 @ Y0 @ Y1 ) @ ( funcSet @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f131,plain,
! [X1: $i] :
( ( ( in @ X1 @ ( funcSet @ sK4 @ sK3 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ X1 @ Y0 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y0 ) ) ) )
=> ( sK2 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f128]) ).
thf(f128,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( funcSet @ sK4 @ sK3 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ Y0 @ Y1 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y1 ) ) ) )
=> ( sK2 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( funcSet @ sK4 @ sK3 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ Y0 @ Y1 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y1 ) ) ) )
=> ( sK2 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f121]) ).
thf(f121,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( funcSet @ sK4 @ sK3 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ Y0 @ Y1 )
= ( ap @ sK4 @ sK3 @ sK2 @ Y1 ) ) ) )
=> ( sK2 = Y0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f115,f71]) ).
thf(f115,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( funcSet @ X1 @ X3 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( funcSet @ X1 @ X3 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( ap @ X1 @ X3 @ Y0 @ Y1 )
= ( ap @ X1 @ X3 @ X2 @ Y1 ) ) ) )
=> ( X2 = Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f114]) ).
thf(f114,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( funcSet @ X1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( funcSet @ X1 @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( ap @ X1 @ Y0 @ Y1 @ Y2 )
= ( ap @ X1 @ Y0 @ X2 @ Y2 ) ) ) )
=> ( X2 = Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( funcSet @ X1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( funcSet @ X1 @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( ap @ X1 @ Y0 @ Y1 @ Y2 )
= ( ap @ X1 @ Y0 @ X2 @ Y2 ) ) ) )
=> ( X2 = Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( funcSet @ X1 @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( funcSet @ X1 @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( ap @ X1 @ Y1 @ Y2 @ Y3 )
= ( ap @ X1 @ Y1 @ Y0 @ Y3 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( funcSet @ X1 @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( funcSet @ X1 @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( ap @ X1 @ Y1 @ Y2 @ Y3 )
= ( ap @ X1 @ Y1 @ Y0 @ Y3 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( funcSet @ Y0 @ Y2 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y2 @ Y3 @ Y4 )
= ( ap @ Y0 @ Y2 @ Y1 @ Y4 ) ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f174,plain,
( ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ sK5 )
= ( ap @ sK4 @ sK3 @ sK2 @ sK5 ) ),
inference(equality_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ( ( ap @ sK4 @ sK3 @ sK2 @ sK5 )
= ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ sK5 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f159]) ).
thf(f159,plain,
( $true
= ( $true
=> ( ( ap @ sK4 @ sK3 @ sK2 @ sK5 )
= ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ sK5 ) ) ) ),
inference(superposition,[status(thm)],[f119,f156]) ).
thf(f119,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ sK2 @ X1 )
= ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ sK2 @ Y0 )
= ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ sK2 @ Y0 )
= ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f95]) ).
thf(f95,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( ( ap @ sK4 @ sK3 @ sK2 @ Y0 )
= ( ap @ sK4 @ sK3 @ ( lam @ sK4 @ sK3 @ ( ap @ sK4 @ sK3 @ sK2 ) ) @ Y0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f89,f75]) ).
thf(f89,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ ( X3 @ Y0 ) @ X2 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ Y0 )
= ( ap @ X1 @ X2 @ ( lam @ X1 @ X2 @ X3 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( $true
= ( ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ ( Y0 @ Y1 ) @ X2 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
= ( ap @ X1 @ X2 @ ( lam @ X1 @ X2 @ Y0 ) @ Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ ( Y0 @ Y1 ) @ X2 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
= ( ap @ X1 @ X2 @ ( lam @ X1 @ X2 @ Y0 ) @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( in @ ( Y1 @ Y2 ) @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y1 @ Y2 )
= ( ap @ X1 @ Y0 @ ( lam @ X1 @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( in @ ( Y1 @ Y2 ) @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y1 @ Y2 )
= ( ap @ X1 @ Y0 @ ( lam @ X1 @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ ( lam @ Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
= ( ap @ Y0 @ Y1 @ ( lam @ Y0 @ Y1 @ Y2 ) @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU699^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:31:16 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : SEU699^2 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.48 % Domain : Set Theory
% 0.32/0.48 % Problem : Functions - Extensionality and Beta Reduction
% 0.32/0.48 % Version : Especial > Reduced > Especial.
% 0.32/0.48 % English : (! A:i.! B:i.! f:i.in f (funcSet A B) ->
% 0.32/0.48 % lam A B (^ x:i.ap A B f x) = f)
% 0.32/0.48
% 0.32/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.48 % Source : [Bro08]
% 0.32/0.48 % Names : ZFC201l [Bro08]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.46 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.22 v7.2.0, 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 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v4.0.1, 0.67 v4.0.0, 1.00 v3.7.0
% 0.32/0.48 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.32/0.48 % Number of atoms : 29 ( 8 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 6 ( 5 avg)
% 0.32/0.48 % Number of connectives : 86 ( 0 ~; 0 |; 0 &; 70 @)
% 0.32/0.48 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 12 ( 3 avg)
% 0.32/0.48 % Number of types : 2 ( 0 usr)
% 0.32/0.48 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 9 ( 8 usr; 4 con; 0-4 aty)
% 0.32/0.48 % Number of variables : 24 ( 3 ^; 21 !; 0 ?; 24 :)
% 0.32/0.48 % SPC : TH0_THM_EQU_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : http://mathgate.info/detsetitem.php?id=251
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 thf(in_type,type,
% 0.32/0.48 in: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcSet_type,type,
% 0.32/0.48 funcSet: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(ap_type,type,
% 0.32/0.48 ap: $i > $i > $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(ap2p_type,type,
% 0.32/0.48 ap2p: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ap2p,definition,
% 0.32/0.48 ( ap2p
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(lam_type,type,
% 0.32/0.48 lam: $i > $i > ( $i > $i ) > $i ).
% 0.32/0.48
% 0.32/0.48 thf(lam2p_type,type,
% 0.32/0.48 lam2p: $o ).
% 0.32/0.48
% 0.32/0.48 thf(lam2p,definition,
% 0.32/0.48 ( lam2p
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.48 => ( in
% 0.32/0.48 @ ( lam @ A @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.32/0.48 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcext2_type,type,
% 0.32/0.48 funcext2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcext2,definition,
% 0.32/0.48 ( funcext2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ! [Xg: $i] :
% 0.32/0.48 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.32/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(beta2_type,type,
% 0.32/0.48 beta2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(beta2,definition,
% 0.32/0.48 ( beta2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B
% 0.32/0.48 @ ( lam @ A @ B
% 0.32/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.32/0.48 @ Xx )
% 0.32/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eta2,conjecture,
% 0.32/0.48 ( ap2p
% 0.32/0.48 => ( lam2p
% 0.32/0.48 => ( funcext2
% 0.32/0.48 => ( beta2
% 0.32/0.48 => ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ( ( lam @ A @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.32/0.48 = Xf ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 1.74/1.43 ---- Embedded in THF ---
% 1.74/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.74/1.43 %%% Generated on Tue Feb 24 12:31:17 EST 2026
% 1.74/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.74/1.43 %%% Logic specification used:
% 1.74/1.43 %%% thf(spec, logic, $$dhol).
% 1.74/1.43
% 1.74/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2DTF2784.p
% See solution above
% 1.74/1.43 ------------------------
% 1.74/1.44 ---- Cleaned THF ---
% 1.74/1.44 thf(in_type,type,
% 1.74/1.44 in: $i > $i > $o ).
% 1.74/1.44
% 1.74/1.44 thf(funcSet_type,type,
% 1.74/1.44 funcSet: $i > $i > $i ).
% 1.74/1.44
% 1.74/1.44 thf(ap_type,type,
% 1.74/1.44 ap: $i > $i > $i > $i > $i ).
% 1.74/1.44
% 1.74/1.44 thf(ap2p_type,type,
% 1.74/1.44 ap2p: $o ).
% 1.74/1.44
% 1.74/1.44 thf(ap2p,definition,
% 1.74/1.44 ( ap2p
% 1.74/1.44 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.74/1.44 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.74/1.44 => ! [Xx: $i] :
% 1.74/1.44 ( ( in @ Xx @ A )
% 1.74/1.44 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 1.74/1.44
% 1.74/1.44 thf(lam_type,type,
% 1.74/1.44 lam: $i > $i > ( $i > $i ) > $i ).
% 1.74/1.44
% 1.74/1.44 thf(lam2p_type,type,
% 1.74/1.44 lam2p: $o ).
% 1.74/1.44
% 1.74/1.44 thf(lam2p,definition,
% 1.74/1.44 ( lam2p
% 1.74/1.44 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 1.74/1.44 ( ! [Xx: $i] :
% 1.74/1.44 ( ( in @ Xx @ A )
% 1.74/1.44 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.74/1.44 => ( in
% 1.74/1.44 @ ( lam @ A @ B
% 1.74/1.44 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 1.74/1.44 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 1.74/1.44
% 1.74/1.44 thf(funcext2_type,type,
% 1.74/1.44 funcext2: $o ).
% 1.74/1.44
% 1.74/1.44 thf(funcext2,definition,
% 1.74/1.44 ( funcext2
% 1.74/1.44 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.74/1.44 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.74/1.44 => ! [Xg: $i] :
% 1.74/1.44 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 1.74/1.44 => ( ! [Xx: $i] :
% 1.74/1.44 ( ( in @ Xx @ A )
% 1.74/1.44 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.74/1.44 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 1.74/1.44 => ( Xf = Xg ) ) ) ) ) ) ).
% 1.74/1.44
% 1.74/1.44 thf(beta2_type,type,
% 1.74/1.44 beta2: $o ).
% 1.74/1.44
% 1.74/1.44 thf(beta2,definition,
% 1.74/1.44 ( beta2
% 1.74/1.44 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 1.74/1.44 ( ! [Xx: $i] :
% 1.74/1.44 ( ( in @ Xx @ A )
% 1.74/1.44 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.74/1.44 => ! [Xx: $i] :
% 1.74/1.44 ( ( in @ Xx @ A )
% 1.74/1.44 => ( ( ap @ A @ B
% 1.74/1.44 @ ( lam @ A @ B
% 1.74/1.44 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 1.74/1.44 @ Xx )
% 1.74/1.44 = ( Xf @ Xx ) ) ) ) ) ) ).
% 1.74/1.44
% 1.74/1.44 thf(eta2,conjecture,
% 1.74/1.44 ( ap2p
% 1.74/1.44 => ( lam2p
% 1.74/1.44 => ( funcext2
% 1.74/1.44 => ( beta2
% 1.74/1.44 => ! [A: $i,B: $i,Xf: $i] :
% 1.74/1.44 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.74/1.44 => ( ( lam @ A @ B
% 1.74/1.44 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 1.74/1.44 = Xf ) ) ) ) ) ) ).
% 1.74/1.44 ------------------------
% 1.74/1.46 % (2891)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/183Mi)
% 1.74/1.46 % (2894)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/2Mi)
% 1.74/1.46 % (2893)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_2784 for (2999ds/27Mi)
% 1.74/1.46 % (2895)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_2784 for (2999ds/2Mi)
% 1.74/1.46 % (2897)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/18Mi)
% 1.74/1.46 % (2892)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_2784 for (2999ds/4Mi)
% 1.74/1.46 % (2896)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_2784 for (2999ds/275Mi)
% 1.74/1.46 % (2894)Instruction limit reached!
% 1.74/1.46 % (2894)------------------------------
% 1.74/1.46 % (2894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (2894)Termination reason: Unknown
% 1.74/1.46 % (2894)Termination phase: Preprocessing 2
% 1.74/1.46 % (2895)Instruction limit reached!
% 1.74/1.46 % (2895)------------------------------
% 1.74/1.46 % (2895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (2895)Termination reason: Unknown
% 1.74/1.46 % (2895)Termination phase: Preprocessing 3
% 1.74/1.46
% 1.74/1.46 % (2895)Memory used [KB]: 1023
% 1.74/1.46 % (2895)Time elapsed: 0.003 s
% 1.74/1.46 % (2895)Instructions burned: 3 (million)
% 1.74/1.46 % (2895)------------------------------
% 1.74/1.46 % (2895)------------------------------
% 1.74/1.46
% 1.74/1.46 % (2894)Memory used [KB]: 1023
% 1.74/1.46 % (2894)Time elapsed: 0.003 s
% 1.74/1.46 % (2894)Instructions burned: 3 (million)
% 1.74/1.46 % (2894)------------------------------
% 1.74/1.46 % (2894)------------------------------
% 1.74/1.47 % (2892)Instruction limit reached!
% 1.74/1.47 % (2892)------------------------------
% 1.74/1.47 % (2892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (2892)Termination reason: Unknown
% 1.74/1.47 % (2892)Termination phase: Saturation
% 1.74/1.47
% 1.74/1.47 % (2892)Memory used [KB]: 1023
% 1.74/1.47 % (2892)Time elapsed: 0.004 s
% 1.74/1.47 % (2892)Instructions burned: 5 (million)
% 1.74/1.47 % (2892)------------------------------
% 1.74/1.47 % (2892)------------------------------
% 1.74/1.47 % (2897)Instruction limit reached!
% 1.74/1.47 % (2897)------------------------------
% 1.74/1.47 % (2897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (2897)Termination reason: Unknown
% 1.74/1.47 % (2897)Termination phase: Saturation
% 1.74/1.47
% 1.74/1.47 % (2897)Memory used [KB]: 5756
% 1.74/1.47 % (2897)Time elapsed: 0.011 s
% 1.74/1.47 % (2897)Instructions burned: 18 (million)
% 1.74/1.47 % (2897)------------------------------
% 1.74/1.47 % (2897)------------------------------
% 1.74/1.48 % (2893)Instruction limit reached!
% 1.74/1.48 % (2893)------------------------------
% 1.74/1.48 % (2893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (2893)Termination reason: Unknown
% 1.74/1.48 % (2893)Termination phase: Saturation
% 1.74/1.48
% 1.74/1.48 % (2893)Memory used [KB]: 5628
% 1.74/1.48 % (2893)Time elapsed: 0.015 s
% 1.74/1.48 % (2893)Instructions burned: 27 (million)
% 1.74/1.48 % (2893)------------------------------
% 1.74/1.48 % (2893)------------------------------
% 1.74/1.48 % (2898)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/3Mi)
% 1.74/1.48 % (2899)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_2784 for (2999ds/37Mi)
% 1.74/1.48 % (2900)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_2784 for (2999ds/15Mi)
% 1.74/1.48 % (2898)Instruction limit reached!
% 1.74/1.48 % (2898)------------------------------
% 1.74/1.48 % (2898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (2898)Termination reason: Unknown
% 1.74/1.48 % (2898)Termination phase: Property scanning
% 1.74/1.48
% 1.74/1.48 % (2898)Memory used [KB]: 1023
% 1.74/1.48 % (2898)Time elapsed: 0.003 s
% 1.74/1.48 % (2898)Instructions burned: 3 (million)
% 1.74/1.48 % (2898)------------------------------
% 1.74/1.48 % (2898)------------------------------
% 1.74/1.49 % (2901)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_2784 for (2999ds/3Mi)
% 1.74/1.49 % (2900)Instruction limit reached!
% 1.74/1.49 % (2900)------------------------------
% 1.74/1.49 % (2900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.49 % (2900)Termination reason: Unknown
% 1.74/1.49 % (2900)Termination phase: Saturation
% 1.74/1.49
% 1.74/1.49 % (2900)Memory used [KB]: 5628
% 1.74/1.49 % (2900)Time elapsed: 0.010 s
% 1.74/1.49 % (2900)Instructions burned: 16 (million)
% 1.74/1.49 % (2900)------------------------------
% 1.74/1.49 % (2900)------------------------------
% 1.74/1.49 % (2901)Instruction limit reached!
% 1.74/1.49 % (2901)------------------------------
% 1.74/1.49 % (2901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.49 % (2901)Termination reason: Unknown
% 1.74/1.49 % (2901)Termination phase: Property scanning
% 1.74/1.49
% 1.74/1.49 % (2901)Memory used [KB]: 1023
% 1.74/1.49 % (2901)Time elapsed: 0.003 s
% 1.74/1.49 % (2901)Instructions burned: 4 (million)
% 1.74/1.49 % (2901)------------------------------
% 1.74/1.49 % (2901)------------------------------
% 1.74/1.49 % (2902)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_2784 for (2999ds/1041Mi)
% 1.81/1.50 % (2903)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/7Mi)
% 1.81/1.50 % (2899)Instruction limit reached!
% 1.81/1.50 % (2899)------------------------------
% 1.81/1.50 % (2899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.50 % (2899)Termination reason: Unknown
% 1.81/1.50 % (2899)Termination phase: Saturation
% 1.81/1.50
% 1.81/1.50 % (2899)Memory used [KB]: 5756
% 1.81/1.50 % (2899)Time elapsed: 0.019 s
% 1.81/1.50 % (2899)Instructions burned: 37 (million)
% 1.81/1.50 % (2899)------------------------------
% 1.81/1.50 % (2899)------------------------------
% 1.81/1.50 % (2903)Instruction limit reached!
% 1.81/1.50 % (2903)------------------------------
% 1.81/1.50 % (2903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.50 % (2903)Termination reason: Unknown
% 1.81/1.50 % (2903)Termination phase: Saturation
% 1.81/1.50
% 1.81/1.50 % (2903)Memory used [KB]: 1023
% 1.81/1.50 % (2903)Time elapsed: 0.005 s
% 1.81/1.50 % (2903)Instructions burned: 8 (million)
% 1.81/1.50 % (2903)------------------------------
% 1.81/1.50 % (2903)------------------------------
% 1.81/1.51 % (2904)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/16Mi)
% 1.81/1.51 % (2905)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_2784 for (2999ds/3Mi)
% 1.81/1.51 % (2905)Instruction limit reached!
% 1.81/1.51 % (2905)------------------------------
% 1.81/1.51 % (2905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.51 % (2905)Termination reason: Unknown
% 1.81/1.51 % (2905)Termination phase: Property scanning
% 1.81/1.51
% 1.81/1.51 % (2905)Memory used [KB]: 1023
% 1.81/1.51 % (2905)Time elapsed: 0.003 s
% 1.81/1.51 % (2905)Instructions burned: 4 (million)
% 1.81/1.51 % (2905)------------------------------
% 1.81/1.51 % (2905)------------------------------
% 1.81/1.51 % (2906)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/3Mi)
% 1.81/1.51 % (2904)Instruction limit reached!
% 1.81/1.51 % (2904)------------------------------
% 1.81/1.51 % (2904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.51 % (2904)Termination reason: Unknown
% 1.81/1.51 % (2904)Termination phase: Saturation
% 1.81/1.51
% 1.81/1.51 % (2904)Memory used [KB]: 5884
% 1.81/1.51 % (2904)Time elapsed: 0.010 s
% 1.81/1.51 % (2904)Instructions burned: 16 (million)
% 1.81/1.51 % (2904)------------------------------
% 1.81/1.51 % (2904)------------------------------
% 1.81/1.52 % (2906)Instruction limit reached!
% 1.81/1.52 % (2906)------------------------------
% 1.81/1.52 % (2906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (2906)Termination reason: Unknown
% 1.81/1.52 % (2906)Termination phase: Property scanning
% 1.81/1.52
% 1.81/1.52 % (2906)Memory used [KB]: 1023
% 1.81/1.52 % (2906)Time elapsed: 0.003 s
% 1.81/1.52 % (2906)Instructions burned: 4 (million)
% 1.81/1.52 % (2906)------------------------------
% 1.81/1.52 % (2906)------------------------------
% 1.81/1.52 % (2907)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/7Mi)
% 1.81/1.52 % (2907)Refutation not found, incomplete strategy
% 1.81/1.52 % (2907)------------------------------
% 1.81/1.52 % (2907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (2907)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.52
% 1.81/1.52
% 1.81/1.52 % (2907)Memory used [KB]: 5500
% 1.81/1.52 % (2907)Time elapsed: 0.004 s
% 1.81/1.52 % (2907)Instructions burned: 6 (million)
% 1.81/1.52 % (2907)------------------------------
% 1.81/1.52 % (2907)------------------------------
% 1.81/1.52 % (2908)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/3Mi)
% 1.81/1.53 % (2908)Instruction limit reached!
% 1.81/1.53 % (2908)------------------------------
% 1.81/1.53 % (2908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.53 % (2908)Termination reason: Unknown
% 1.81/1.53 % (2908)Termination phase: Property scanning
% 1.81/1.53
% 1.81/1.53 % (2908)Memory used [KB]: 1023
% 1.81/1.53 % (2908)Time elapsed: 0.003 s
% 1.81/1.53 % (2908)Instructions burned: 4 (million)
% 1.81/1.53 % (2908)------------------------------
% 1.81/1.53 % (2908)------------------------------
% 1.81/1.53 % (2902)First to succeed.
% 1.81/1.53 % (2909)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/4Mi)
% 1.81/1.53 % (2910)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2784 for (2999ds/18Mi)
% 1.81/1.53 % (2909)Instruction limit reached!
% 1.81/1.53 % (2909)------------------------------
% 1.81/1.53 % (2909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.53 % (2909)Termination reason: Unknown
% 1.81/1.53 % (2909)Termination phase: Saturation
% 1.81/1.53
% 1.81/1.53 % (2909)Memory used [KB]: 5500
% 1.81/1.53 % (2909)Time elapsed: 0.004 s
% 1.81/1.53 % (2909)Instructions burned: 5 (million)
% 1.81/1.53 % (2909)------------------------------
% 1.81/1.53 % (2909)------------------------------
% 1.81/1.54 % (2902)Refutation found. Thanks to Tanya!
% 1.81/1.54 % SZS status Theorem for DTF2THF_2784
% 1.81/1.54 % SZS output start Proof for DTF2THF_2784
% 1.81/1.54 thf(func_def_0, type, in: $i > $i > $o).
% 1.81/1.54 thf(func_def_1, type, funcSet: $i > $i > $i).
% 1.81/1.54 thf(func_def_2, type, ap: $i > $i > $i > $i > $i).
% 1.81/1.54 thf(func_def_5, type, lam: $i > $i > ($i > $i) > $i).
% 1.81/1.54 thf(func_def_22, type, ph1: !>[X0: $tType]:(X0)).
% 1.81/1.54 thf(f177,plain,(
% 1.81/1.54 $false),
% 1.81/1.54 inference(subsumption_resolution,[status(thm)],[f174,f165])).
% 1.81/1.54 thf(f165,plain,(
% 1.81/1.54 ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ sK5) != (ap @ sK4 @ sK3 @ sK2 @ sK5))),
% 1.81/1.54 inference(equality_proxy_clausification,[status(thm)],[f158])).
% 1.81/1.54 thf(f158,plain,(
% 1.81/1.54 ($false = ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ sK5) = (ap @ sK4 @ sK3 @ sK2 @ sK5)))),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f157])).
% 1.81/1.54 thf(f157,plain,(
% 1.81/1.54 ($false = ($true => ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ sK5) = (ap @ sK4 @ sK3 @ sK2 @ sK5))))),
% 1.81/1.54 inference(backward_demodulation,[status(thm)],[f154,f156])).
% 1.81/1.54 thf(f156,plain,(
% 1.81/1.54 ((in @ sK5 @ sK4) = $true)),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 1.81/1.54 thf(f154,plain,(
% 1.81/1.54 ($false = ((in @ sK5 @ sK4) => ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ sK5) = (ap @ sK4 @ sK3 @ sK2 @ sK5))))),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f150])).
% 1.81/1.54 thf(f150,plain,(
% 1.81/1.54 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0) = (ap @ sK4 @ sK3 @ sK2 @ Y0)))) @ sK5))),
% 1.81/1.54 inference(sigma_clausification,[status(thm)],[f147])).
% 1.81/1.54 thf(f147,plain,(
% 1.81/1.54 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0) = (ap @ sK4 @ sK3 @ sK2 @ Y0))))))),
% 1.81/1.54 inference(not_proxy_clausification,[status(thm)],[f144])).
% 1.81/1.54 thf(f144,plain,(
% 1.81/1.54 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0) = (ap @ sK4 @ sK3 @ sK2 @ Y0)))))) = $true)),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f143])).
% 1.81/1.54 thf(f143,plain,(
% 1.81/1.54 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0) = (ap @ sK4 @ sK3 @ sK2 @ Y0))))) => $false))),
% 1.81/1.54 inference(forward_demodulation,[status(thm)],[f142,f73])).
% 1.81/1.54 thf(f73,plain,(
% 1.81/1.54 ($false = (sK2 = (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2))))),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f72])).
% 1.81/1.54 thf(f72,plain,(
% 1.81/1.54 ($false = ($true => (sK2 = (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)))))),
% 1.81/1.54 inference(backward_demodulation,[status(thm)],[f69,f71])).
% 1.81/1.54 thf(f71,plain,(
% 1.81/1.54 ((in @ sK2 @ (funcSet @ sK4 @ sK3)) = $true)),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.81/1.54 thf(f69,plain,(
% 1.81/1.54 (((in @ sK2 @ (funcSet @ sK4 @ sK3)) => (sK2 = (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)))) = $false)),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.81/1.54 thf(f68,plain,(
% 1.81/1.54 (((^[Y0 : $i]: ((in @ sK2 @ (funcSet @ Y0 @ sK3)) => (sK2 = (lam @ Y0 @ sK3 @ (ap @ Y0 @ sK3 @ sK2))))) @ sK4) = $false)),
% 1.81/1.54 inference(sigma_clausification,[status(thm)],[f67])).
% 1.81/1.54 thf(f67,plain,(
% 1.81/1.54 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ sK2 @ (funcSet @ Y0 @ sK3)) => (sK2 = (lam @ Y0 @ sK3 @ (ap @ Y0 @ sK3 @ sK2)))))))),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.81/1.54 thf(f66,plain,(
% 1.81/1.54 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ sK2 @ (funcSet @ Y1 @ Y0)) => (sK2 = (lam @ Y1 @ Y0 @ (ap @ Y1 @ Y0 @ sK2))))))) @ sK3))),
% 1.81/1.54 inference(sigma_clausification,[status(thm)],[f65])).
% 1.81/1.54 thf(f65,plain,(
% 1.81/1.54 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ sK2 @ (funcSet @ Y1 @ Y0)) => (sK2 = (lam @ Y1 @ Y0 @ (ap @ Y1 @ Y0 @ sK2)))))))))),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.81/1.54 thf(f64,plain,(
% 1.81/1.54 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0))))))))) @ sK2))),
% 1.81/1.54 inference(sigma_clausification,[status(thm)],[f58])).
% 1.81/1.54 thf(f58,plain,(
% 1.81/1.54 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0)))))))))))),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.81/1.54 thf(f57,plain,(
% 1.81/1.54 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0))))))))))))),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f56])).
% 1.81/1.54 thf(f56,plain,(
% 1.81/1.54 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0)))))))))))) = $false)),
% 1.81/1.54 inference(backward_demodulation,[status(thm)],[f41,f55])).
% 1.81/1.54 thf(f55,plain,(
% 1.81/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3)))))))))))))),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.81/1.54 thf(f41,plain,(
% 1.81/1.54 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0)))))))))))))),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.81/1.54 thf(f28,plain,(
% 1.81/1.54 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (in @ (lam @ Y2 @ Y0 @ Y1) @ (funcSet @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0))))))))))))))),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.81/1.54 thf(f25,plain,(
% 1.81/1.54 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (in @ (lam @ Y2 @ Y0 @ Y1) @ (funcSet @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0)))))))))))))))),
% 1.81/1.54 inference(not_proxy_clausification,[status(thm)],[f24])).
% 1.81/1.54 thf(f24,plain,(
% 1.81/1.54 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (in @ (lam @ Y2 @ Y0 @ Y1) @ (funcSet @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0))))))))))))))))),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.81/1.54 thf(f23,plain,(
% 1.81/1.54 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (in @ (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))) @ (funcSet @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (^[Y3 : $i]: (ap @ Y2 @ Y1 @ Y0 @ Y3)))))))))))))))))),
% 1.81/1.54 inference(definition_unfolding,[status(thm)],[f21,f20,f19,f22,f18])).
% 1.81/1.54 thf(f18,plain,(
% 1.81/1.54 (beta2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3)))))))))))))),
% 1.81/1.54 inference(cnf_transformation,[status(thm)],[f11])).
% 1.81/1.54 thf(f11,plain,(
% 1.81/1.54 (beta2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3)))))))))))))),
% 1.81/1.54 inference(fool_elimination,[status(thm)],[f10])).
% 1.81/1.54 thf(f10,plain,(
% 1.81/1.54 (beta2 = ! [X0 : $i > $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => ! [X4 : $i] : ((in @ X4 @ X2) => ((X0 @ X4) = (ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[X5 : $i] : (X0 @ X5))) @ X4)))))),
% 1.81/1.54 inference(rectify,[status(thm)],[f4])).
% 1.81/1.54 thf(f4,axiom,(
% 1.81/1.54 (beta2 = ! [X2 : $i > $i,X1 : $i,X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X2 @ X3) = (ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X5 : $i] : (X2 @ X5))) @ X3)))))),
% 1.81/1.54 file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',beta2)).
% 1.81/1.54 thf(f22,plain,(
% 1.81/1.54 (funcext2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3)))))))))))))),
% 1.81/1.54 inference(cnf_transformation,[status(thm)],[f9])).
% 1.81/1.54 thf(f9,plain,(
% 1.81/1.54 (funcext2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3)))))))))))))),
% 1.81/1.54 inference(fool_elimination,[status(thm)],[f8])).
% 1.81/1.54 thf(f8,plain,(
% 1.81/1.54 (funcext2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X2 @ X0)) => (! [X4 : $i] : ((in @ X4 @ X2) => ((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4))) => (X1 = X3)))))),
% 1.81/1.54 inference(rectify,[status(thm)],[f3])).
% 1.81/1.54 thf(f3,axiom,(
% 1.81/1.54 (funcext2 = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X4 : $i] : ((in @ X4 @ (funcSet @ X0 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ X2 @ X3) = (ap @ X0 @ X1 @ X4 @ X3))) => (X2 = X4)))))),
% 1.81/1.54 file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',funcext2)).
% 1.81/1.54 thf(f19,plain,(
% 1.81/1.54 (lam2p = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (in @ (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))) @ (funcSet @ Y2 @ Y0))))))))))),
% 1.81/1.54 inference(cnf_transformation,[status(thm)],[f17])).
% 1.81/1.54 thf(f17,plain,(
% 1.81/1.54 (lam2p = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (in @ (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))) @ (funcSet @ Y2 @ Y0))))))))))),
% 1.81/1.54 inference(fool_elimination,[status(thm)],[f16])).
% 1.81/1.54 thf(f16,plain,(
% 1.81/1.54 (lam2p = ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X1 @ X3) @ X2)) => (in @ (lam @ X0 @ X2 @ (^[X4 : $i] : (X1 @ X4))) @ (funcSet @ X0 @ X2))))),
% 1.81/1.54 inference(rectify,[status(thm)],[f2])).
% 1.81/1.54 thf(f2,axiom,(
% 1.81/1.54 (lam2p = ! [X0 : $i,X2 : $i > $i,X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (in @ (lam @ X0 @ X1 @ (^[X3 : $i] : (X2 @ X3))) @ (funcSet @ X0 @ X1))))),
% 1.81/1.54 file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',lam2p)).
% 1.81/1.54 thf(f20,plain,(
% 1.81/1.54 (ap2p = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))))),
% 1.81/1.54 inference(cnf_transformation,[status(thm)],[f15])).
% 1.81/1.54 thf(f15,plain,(
% 1.81/1.54 (ap2p = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))))),
% 1.81/1.54 inference(fool_elimination,[status(thm)],[f14])).
% 1.81/1.54 thf(f14,plain,(
% 1.81/1.54 (ap2p = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X2 @ X1 @ X3) @ X2))))),
% 1.81/1.54 inference(rectify,[status(thm)],[f1])).
% 1.81/1.54 thf(f1,axiom,(
% 1.81/1.54 (ap2p = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))))),
% 1.81/1.54 file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',ap2p)).
% 1.81/1.54 thf(f21,plain,(
% 1.81/1.54 ((~ (ap2p => (lam2p => (funcext2 => (beta2 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (^[Y3 : $i]: (ap @ Y2 @ Y1 @ Y0 @ Y3)))))))))))))))) = $true)),
% 1.81/1.54 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.54 thf(f13,plain,(
% 1.81/1.54 ((~ (ap2p => (lam2p => (funcext2 => (beta2 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (Y0 = (lam @ Y2 @ Y1 @ (^[Y3 : $i]: (ap @ Y2 @ Y1 @ Y0 @ Y3)))))))))))))))) = $true)),
% 1.81/1.54 inference(fool_elimination,[status(thm)],[f12])).
% 1.81/1.54 thf(f12,plain,(
% 1.81/1.54 ~(ap2p => (lam2p => (funcext2 => (beta2 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (X2 = (lam @ X0 @ X1 @ (^[X3 : $i] : (ap @ X0 @ X1 @ X2 @ X3)))))))))),
% 1.81/1.54 inference(rectify,[status(thm)],[f6])).
% 1.81/1.54 thf(f6,negated_conjecture,(
% 1.81/1.54 ~(ap2p => (lam2p => (funcext2 => (beta2 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (X2 = (lam @ X0 @ X1 @ (^[X3 : $i] : (ap @ X0 @ X1 @ X2 @ X3)))))))))),
% 1.81/1.54 inference(negated_conjecture,[status(cth)],[f5])).
% 1.81/1.54 thf(f5,conjecture,(
% 1.81/1.54 ap2p => (lam2p => (funcext2 => (beta2 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (X2 = (lam @ X0 @ X1 @ (^[X3 : $i] : (ap @ X0 @ X1 @ X2 @ X3))))))))),
% 1.81/1.54 file('/export/starexec/sandbox/tmp/tmp.IXMZ6PZqaD/DTF2THF_2784.p',eta2)).
% 1.81/1.54 thf(f142,plain,(
% 1.81/1.54 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0) = (ap @ sK4 @ sK3 @ sK2 @ Y0))))) => (sK2 = (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)))))),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f136])).
% 1.81/1.54 thf(f136,plain,(
% 1.81/1.54 ($true = ($true => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0) = (ap @ sK4 @ sK3 @ sK2 @ Y0))))) => (sK2 = (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2))))))),
% 1.81/1.54 inference(superposition,[status(thm)],[f131,f84])).
% 1.81/1.54 thf(f84,plain,(
% 1.81/1.54 ($true = (in @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ (funcSet @ sK4 @ sK3)))),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f81])).
% 1.81/1.54 thf(f81,plain,(
% 1.81/1.54 ($true = ($true => (in @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ (funcSet @ sK4 @ sK3))))),
% 1.81/1.54 inference(superposition,[status(thm)],[f52,f75])).
% 1.81/1.54 thf(f75,plain,(
% 1.81/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (in @ (ap @ sK4 @ sK3 @ sK2 @ Y0) @ sK3)))))),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f74])).
% 1.81/1.54 thf(f74,plain,(
% 1.81/1.54 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (in @ (ap @ sK4 @ sK3 @ sK2 @ Y0) @ sK3))))))),
% 1.81/1.54 inference(superposition,[status(thm)],[f39,f71])).
% 1.81/1.54 thf(f39,plain,(
% 1.81/1.54 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ (funcSet @ X3 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (ap @ X3 @ X1 @ X2 @ Y0) @ X1))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.81/1.54 thf(f38,plain,(
% 1.81/1.54 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ (funcSet @ Y0 @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (ap @ Y0 @ X1 @ X2 @ Y1) @ X1)))))) @ X3))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f37])).
% 1.81/1.54 thf(f37,plain,(
% 1.81/1.54 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (funcSet @ Y0 @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (ap @ Y0 @ X1 @ X2 @ Y1) @ X1))))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.81/1.54 thf(f36,plain,(
% 1.81/1.54 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (funcSet @ Y1 @ X1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (ap @ Y1 @ X1 @ Y0 @ Y2) @ X1)))))))) @ X2))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f35])).
% 1.81/1.54 thf(f35,plain,(
% 1.81/1.54 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (funcSet @ Y1 @ X1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (ap @ Y1 @ X1 @ Y0 @ Y2) @ X1))))))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.81/1.54 thf(f34,plain,(
% 1.81/1.54 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0)))))))))) @ X1))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f29])).
% 1.81/1.54 thf(f29,plain,(
% 1.81/1.54 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))) = $true)),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.81/1.54 thf(f52,plain,(
% 1.81/1.54 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (X2 @ Y0) @ X1)))) => (in @ (lam @ X3 @ X1 @ X2) @ (funcSet @ X3 @ X1))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.81/1.54 thf(f51,plain,(
% 1.81/1.54 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (X2 @ Y1) @ X1)))) => (in @ (lam @ Y0 @ X1 @ X2) @ (funcSet @ Y0 @ X1)))) @ X3) = $true)) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f50])).
% 1.81/1.54 thf(f50,plain,(
% 1.81/1.54 ( ! [X2 : $i > $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (X2 @ Y1) @ X1)))) => (in @ (lam @ Y0 @ X1 @ X2) @ (funcSet @ Y0 @ X1))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.81/1.54 thf(f49,plain,(
% 1.81/1.54 ( ! [X2 : $i > $i,X1 : $i] : (($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (Y0 @ Y2) @ X1)))) => (in @ (lam @ Y1 @ X1 @ Y0) @ (funcSet @ Y1 @ X1)))))) @ X2))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f48])).
% 1.81/1.54 thf(f48,plain,(
% 1.81/1.54 ( ! [X1 : $i] : (($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (Y0 @ Y2) @ X1)))) => (in @ (lam @ Y1 @ X1 @ Y0) @ (funcSet @ Y1 @ X1))))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.81/1.54 thf(f47,plain,(
% 1.81/1.54 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (in @ (lam @ Y2 @ Y0 @ Y1) @ (funcSet @ Y2 @ Y0)))))))) @ X1))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f42])).
% 1.81/1.54 thf(f42,plain,(
% 1.81/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (in @ (lam @ Y2 @ Y0 @ Y1) @ (funcSet @ Y2 @ Y0))))))))))),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.81/1.54 thf(f131,plain,(
% 1.81/1.54 ( ! [X1 : $i] : ((((in @ X1 @ (funcSet @ sK4 @ sK3)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ X1 @ Y0) = (ap @ sK4 @ sK3 @ sK2 @ Y0))))) => (sK2 = X1))) = $true)) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f128])).
% 1.81/1.54 thf(f128,plain,(
% 1.81/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (funcSet @ sK4 @ sK3)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((ap @ sK4 @ sK3 @ Y0 @ Y1) = (ap @ sK4 @ sK3 @ sK2 @ Y1))))) => (sK2 = Y0)))) @ X1) = $true)) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f126])).
% 1.81/1.54 thf(f126,plain,(
% 1.81/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (funcSet @ sK4 @ sK3)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((ap @ sK4 @ sK3 @ Y0 @ Y1) = (ap @ sK4 @ sK3 @ sK2 @ Y1))))) => (sK2 = Y0))))))),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f121])).
% 1.81/1.54 thf(f121,plain,(
% 1.81/1.54 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (funcSet @ sK4 @ sK3)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((ap @ sK4 @ sK3 @ Y0 @ Y1) = (ap @ sK4 @ sK3 @ sK2 @ Y1))))) => (sK2 = Y0)))))))),
% 1.81/1.54 inference(superposition,[status(thm)],[f115,f71])).
% 1.81/1.54 thf(f115,plain,(
% 1.81/1.54 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ (funcSet @ X1 @ X3)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (funcSet @ X1 @ X3)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((ap @ X1 @ X3 @ Y0 @ Y1) = (ap @ X1 @ X3 @ X2 @ Y1))))) => (X2 = Y0)))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f114])).
% 1.81/1.54 thf(f114,plain,(
% 1.81/1.54 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ (funcSet @ X1 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (funcSet @ X1 @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((ap @ X1 @ Y0 @ Y1 @ Y2) = (ap @ X1 @ Y0 @ X2 @ Y2))))) => (X2 = Y1))))))) @ X3))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f109])).
% 1.81/1.54 thf(f109,plain,(
% 1.81/1.54 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (funcSet @ X1 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (funcSet @ X1 @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((ap @ X1 @ Y0 @ Y1 @ Y2) = (ap @ X1 @ Y0 @ X2 @ Y2))))) => (X2 = Y1)))))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.81/1.54 thf(f108,plain,(
% 1.81/1.54 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (funcSet @ X1 @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ X1 @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((ap @ X1 @ Y1 @ Y2 @ Y3) = (ap @ X1 @ Y1 @ Y0 @ Y3))))) => (Y0 = Y2))))))))) @ X2))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f106])).
% 1.81/1.54 thf(f106,plain,(
% 1.81/1.54 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (funcSet @ X1 @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ X1 @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((ap @ X1 @ Y1 @ Y2 @ Y3) = (ap @ X1 @ Y1 @ Y0 @ Y3))))) => (Y0 = Y2)))))))))) = $true)) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.81/1.54 thf(f105,plain,(
% 1.81/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (funcSet @ Y0 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((ap @ Y0 @ Y2 @ Y3 @ Y4) = (ap @ Y0 @ Y2 @ Y1 @ Y4))))) => (Y1 = Y3))))))))))) @ X1) = $true)) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f55])).
% 1.81/1.54 thf(f174,plain,(
% 1.81/1.54 ((ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ sK5) = (ap @ sK4 @ sK3 @ sK2 @ sK5))),
% 1.81/1.54 inference(equality_proxy_clausification,[status(thm)],[f163])).
% 1.81/1.54 thf(f163,plain,(
% 1.81/1.54 (((ap @ sK4 @ sK3 @ sK2 @ sK5) = (ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ sK5)) = $true)),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f159])).
% 1.81/1.54 thf(f159,plain,(
% 1.81/1.54 ($true = ($true => ((ap @ sK4 @ sK3 @ sK2 @ sK5) = (ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ sK5))))),
% 1.81/1.54 inference(superposition,[status(thm)],[f119,f156])).
% 1.81/1.54 thf(f119,plain,(
% 1.81/1.54 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK4) => ((ap @ sK4 @ sK3 @ sK2 @ X1) = (ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ X1))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.81/1.54 thf(f116,plain,(
% 1.81/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ sK2 @ Y0) = (ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0)))) @ X1) = $true)) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f96])).
% 1.81/1.54 thf(f96,plain,(
% 1.81/1.54 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ sK2 @ Y0) = (ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0))))) = $true)),
% 1.81/1.54 inference(boolean_simplification,[status(thm)],[f95])).
% 1.81/1.54 thf(f95,plain,(
% 1.81/1.54 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK3 @ sK2 @ Y0) = (ap @ sK4 @ sK3 @ (lam @ sK4 @ sK3 @ (ap @ sK4 @ sK3 @ sK2)) @ Y0)))))))),
% 1.81/1.54 inference(superposition,[status(thm)],[f89,f75])).
% 1.81/1.54 thf(f89,plain,(
% 1.81/1.54 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (X3 @ Y0) @ X2)))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X3 @ Y0) = (ap @ X1 @ X2 @ (lam @ X1 @ X2 @ X3) @ Y0)))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.81/1.54 thf(f88,plain,(
% 1.81/1.54 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : (($true = ((^[Y0 : $i > $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (Y0 @ Y1) @ X2)))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) = (ap @ X1 @ X2 @ (lam @ X1 @ X2 @ Y0) @ Y1))))))) @ X3))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f86])).
% 1.81/1.54 thf(f86,plain,(
% 1.81/1.54 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (Y0 @ Y1) @ X2)))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) = (ap @ X1 @ X2 @ (lam @ X1 @ X2 @ Y0) @ Y1)))))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.81/1.54 thf(f85,plain,(
% 1.81/1.54 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (Y1 @ Y2) @ Y0)))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y1 @ Y2) = (ap @ X1 @ Y0 @ (lam @ X1 @ Y0 @ Y1) @ Y2))))))))) @ X2))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f78])).
% 1.81/1.54 thf(f78,plain,(
% 1.81/1.54 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (Y1 @ Y2) @ Y0)))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y1 @ Y2) = (ap @ X1 @ Y0 @ (lam @ X1 @ Y0 @ Y1) @ Y2)))))))))))) )),
% 1.81/1.54 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.81/1.54 thf(f77,plain,(
% 1.81/1.54 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3))))))))))) @ X1))) )),
% 1.81/1.54 inference(pi_clausification,[status(thm)],[f59])).
% 1.81/1.54 thf(f59,plain,(
% 1.81/1.54 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3)))))))))))) = $true)),
% 1.81/1.54 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.81/1.54 % SZS output end Proof for DTF2THF_2784
% 1.81/1.54 % (2902)------------------------------
% 1.81/1.54 % (2902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.54 % (2902)Termination reason: Refutation
% 1.81/1.54
% 1.81/1.54 % (2902)Memory used [KB]: 6012
% 1.81/1.54 % (2902)Time elapsed: 0.043 s
% 1.81/1.54 % (2902)Instructions burned: 74 (million)
% 1.81/1.54 % (2902)------------------------------
% 1.81/1.54 % (2902)------------------------------
% 1.81/1.54 % (2890)Success in time 0.081 s
%------------------------------------------------------------------------------