%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU696^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 09:36:28 AM UTC 2026
% Result : Theorem 1.69s 1.39s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 6
% Syntax : Number of formulae : 89 ( 86 unt; 0 typ; 0 def)
% Number of atoms : 1012 ( 231 equ; 51 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 2460 ( 7 ~; 0 |; 0 &;1926 @)
% ( 0 <=>; 267 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 11 con; 0-4 aty)
% ( 260 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 480 ( 385 ^; 95 !; 0 ?; 480 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_2,type,
func: $i > $i > $i > $o ).
thf(func_def_3,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_6,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_24,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f154,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f150,f79]) ).
thf(f79,plain,
( ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) )
!= sK4 ),
inference(equality_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( $false
= ( ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) )
= sK4 ) ),
inference(boolean_simplification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true
=> ( ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) )
= sK4 ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f72,f74]) ).
thf(f74,plain,
( ( func @ sK2 @ sK3 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
= ( ( func @ sK2 @ sK3 @ sK4 )
=> ( ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) )
= sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ^ [Y0: $i] :
( ( func @ sK2 @ sK3 @ Y0 )
=> ( ( dpsetconstr @ sK2 @ sK3
@ ^ [Y1: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ Y0 @ Y1 ) ) )
= Y0 ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ sK2 @ sK3 @ Y0 )
=> ( ( dpsetconstr @ sK2 @ sK3
@ ^ [Y1: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ Y0 @ Y1 ) ) )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ sK2 @ Y0 @ Y1 )
=> ( ( dpsetconstr @ sK2 @ Y0
@ ^ [Y2: $i] : ( (=) @ ( ap @ sK2 @ Y0 @ Y1 @ Y2 ) ) )
= Y1 ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ sK2 @ Y0 @ Y1 )
=> ( ( dpsetconstr @ sK2 @ Y0
@ ^ [Y2: $i] : ( (=) @ ( ap @ sK2 @ Y0 @ Y1 @ Y2 ) ) )
= Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f62,f64]) ).
thf(f64,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 )
=> ( ( ap @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y4: $i] : ( (=) @ ( Y2 @ Y4 ) ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,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 )
=> ( ( ap @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y4: $i] : ( (=) @ ( Y2 @ Y4 ) ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f61]) ).
thf(f61,plain,
( $false
= ( $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 )
=> ( ( ap @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y4: $i] : ( (=) @ ( Y2 @ Y4 ) ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f46,f60]) ).
thf(f60,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = 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 )
=> ( ( ap @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y4: $i] : ( (=) @ ( Y2 @ Y4 ) ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $false
= ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( dpsetconstr @ Y1 @ Y2
@ ^ [Y3: $i] : ( (=) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = 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 )
=> ( ( ap @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y4: $i] : ( (=) @ ( Y2 @ Y4 ) ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( dpsetconstr @ Y1 @ Y2
@ ^ [Y3: $i] : ( (=) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = 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 )
=> ( ( ap @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y4: $i] : ( (=) @ ( Y2 @ Y4 ) ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( dpsetconstr @ Y1 @ Y2
@ ^ [Y3: $i] : ( (=) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = 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 )
=> ( ( ap @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y4: $i] : ( (=) @ ( Y2 @ Y4 ) ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] : ( (=) @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) )
= Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i] :
( dpsetconstr @ Y3 @ Y4
@ ^ [Y6: $i,Y7: $i] :
( ( Y5 @ Y6 )
= Y7 ) )
@ Y1
@ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = 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 )
=> ( ( ap @ Y0 @ Y1
@ ( ^ [Y4: $i,Y5: $i,Y6: $i > $i] :
( dpsetconstr @ Y4 @ Y5
@ ^ [Y7: $i,Y8: $i] :
( ( Y6 @ Y7 )
= Y8 ) )
@ Y0
@ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( ^ [Y3: $i,Y4: $i,Y5: $i > $i] :
( dpsetconstr @ Y3 @ Y4
@ ^ [Y6: $i,Y7: $i] :
( ( Y5 @ Y6 )
= Y7 ) )
@ Y0
@ Y1
@ ^ [Y3: $i] : ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) )
= Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f22,f24,f26,f25,f27,f21]) ).
thf(f21,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( lam
= ( ^ [X0: $i,X1: $i,X2: $i > $i] :
( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] :
( ( X2 @ X3 )
= X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',lam) ).
thf(f27,plain,
( beta1
= ( !! @ $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 )
=> ( ( ap @ Y0 @ Y1
@ ( ^ [Y4: $i,Y5: $i,Y6: $i > $i] :
( dpsetconstr @ Y4 @ Y5
@ ^ [Y7: $i,Y8: $i] :
( ( Y6 @ Y7 )
= Y8 ) )
@ Y0
@ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f21]) ).
thf(f20,plain,
( beta1
= ( !! @ $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 )
=> ( ( ap @ Y0 @ Y1
@ ( lam @ Y0 @ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( beta1
= ( !! @ $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 )
=> ( ( ap @ Y0 @ Y1
@ ( lam @ Y0 @ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( X0 @ X3 ) @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ap @ X2 @ X1
@ ( lam @ X2 @ X1
@ ^ [X5: $i] : ( X0 @ X5 ) )
@ X4 )
= ( X0 @ X4 ) ) ) )
= beta1 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: $i > $i,X1: $i,X0: $i] :
( ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) )
@ X3 )
= ( X2 @ X3 ) ) ) )
= beta1 ),
file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',beta1) ).
thf(f25,plain,
( funcext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( funcext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( funcext
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( func @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X3 @ X4 )
= ( ap @ X0 @ X1 @ X2 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( funcext
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X5: $i] :
( ( func @ X0 @ X1 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X5 @ X3 ) ) )
=> ( X2 = X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',funcext) ).
thf(f26,plain,
( lamp
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i] :
( dpsetconstr @ Y3 @ Y4
@ ^ [Y6: $i,Y7: $i] :
( ( Y5 @ Y6 )
= Y7 ) )
@ Y1
@ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f21]) ).
thf(f23,plain,
( lamp
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( lam @ Y1 @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( lamp
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( lam @ Y1 @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( lamp
= ( ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( X2 @ X3 ) @ X0 ) )
=> ( func @ X1 @ X0
@ ( lam @ X1 @ X0
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( lamp
= ( ! [X1: $i,X0: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( func @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',lamp) ).
thf(f24,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( app
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( ap @ X2 @ X0 @ X1 @ X3 ) @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( app
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',app) ).
thf(f22,plain,
( ( ~ ( app
=> ( lamp
=> ( funcext
=> ( beta1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( lam @ Y0 @ Y1
@ ^ [Y3: $i] : ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) )
= Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ~ ( app
=> ( lamp
=> ( funcext
=> ( beta1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( ( lam @ Y0 @ Y1
@ ^ [Y3: $i] : ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) )
= Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( app
=> ( lamp
=> ( funcext
=> ( beta1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X1 @ X0 )
=> ( ( lam @ X2 @ X1
@ ^ [X3: $i] : ( ap @ X2 @ X1 @ X0 @ X3 ) )
= X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( app
=> ( lamp
=> ( funcext
=> ( beta1
=> ! [X2: $i,X1: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( ap @ X0 @ X1 @ X2 @ X3 ) )
= X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( app
=> ( lamp
=> ( funcext
=> ( beta1
=> ! [X2: $i,X1: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( ap @ X0 @ X1 @ X2 @ X3 ) )
= X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',eta1) ).
thf(f150,plain,
( ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) )
= sK4 ),
inference(equality_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( $true
= ( sK4
= ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f146]) ).
thf(f146,plain,
( ( $true
=> ( sK4
= ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f141,f83]) ).
thf(f83,plain,
( $true
= ( func @ sK2 @ sK3
@ ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f82]) ).
thf(f82,plain,
( $true
= ( $true
=> ( func @ sK2 @ sK3
@ ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f57,f78]) ).
thf(f78,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( in @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) @ sK3 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( in @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) @ sK3 ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f44,f74]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( func @ X1 @ X3 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ ( ap @ X1 @ X3 @ X2 @ Y0 ) @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( func @ X1 @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ ( ap @ X1 @ Y0 @ X2 @ Y1 ) @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ X1 @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ ( ap @ X1 @ Y0 @ X2 @ Y1 ) @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( in @ ( ap @ X1 @ Y1 @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( in @ ( ap @ X1 @ Y1 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( X1 @ Y0 ) @ X3 ) ) )
=> ( func @ X2 @ X3
@ ( dpsetconstr @ X2 @ X3
@ ^ [Y0: $i] : ( (=) @ ( X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( X1 @ Y1 ) @ Y0 ) ) )
=> ( func @ X2 @ Y0
@ ( dpsetconstr @ X2 @ Y0
@ ^ [Y1: $i] : ( (=) @ ( X1 @ Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i > $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( X1 @ Y1 ) @ Y0 ) ) )
=> ( func @ X2 @ Y0
@ ( dpsetconstr @ X2 @ Y0
@ ^ [Y1: $i] : ( (=) @ ( X1 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X1: $i > $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( X1 @ Y2 ) @ Y1 ) ) )
=> ( func @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y2: $i] : ( (=) @ ( X1 @ Y2 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i > $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( X1 @ Y2 ) @ Y1 ) ) )
=> ( func @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y2: $i] : ( (=) @ ( X1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i > $i] :
( $true
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( dpsetconstr @ Y1 @ Y2
@ ^ [Y3: $i] : ( (=) @ ( Y0 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y0 @ Y3 ) @ Y2 ) ) )
=> ( func @ Y1 @ Y2
@ ( dpsetconstr @ Y1 @ Y2
@ ^ [Y3: $i] : ( (=) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f141,plain,
( ( ( func @ sK2 @ sK3
@ ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) )
=> ( sK4
= ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f136]) ).
thf(f136,plain,
( $true
= ( ( func @ sK2 @ sK3
@ ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) )
=> ( $true
=> ( sK4
= ( dpsetconstr @ sK2 @ sK3
@ ^ [Y0: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f133,f107]) ).
thf(f107,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( ap @ sK2 @ sK3
@ ( dpsetconstr @ sK2 @ sK3
@ ^ [Y1: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y1 ) ) )
@ Y0 )
= ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( ap @ sK2 @ sK3
@ ( dpsetconstr @ sK2 @ sK3
@ ^ [Y1: $i] : ( (=) @ ( ap @ sK2 @ sK3 @ sK4 @ Y1 ) ) )
@ Y0 )
= ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f102,f78]) ).
thf(f102,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ ( X3 @ Y0 ) @ X2 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( ap @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y1: $i] : ( (=) @ ( X3 @ Y1 ) ) )
@ Y0 )
= ( X3 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f101]) ).
thf(f101,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 )
=> ( ( ap @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y2: $i] : ( (=) @ ( Y0 @ Y2 ) ) )
@ Y1 )
= ( Y0 @ Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f94]) ).
thf(f94,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 )
=> ( ( ap @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y2: $i] : ( (=) @ ( Y0 @ Y2 ) ) )
@ Y1 )
= ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,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 )
=> ( ( ap @ X1 @ Y0
@ ( dpsetconstr @ X1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y1 @ Y3 ) ) )
@ Y2 )
= ( Y1 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f88]) ).
thf(f88,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 )
=> ( ( ap @ X1 @ Y0
@ ( dpsetconstr @ X1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y1 @ Y3 ) ) )
@ Y2 )
= ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: $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 )
=> ( ( ap @ Y0 @ Y1
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y4: $i] : ( (=) @ ( Y2 @ Y4 ) ) )
@ Y3 )
= ( Y2 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f133,plain,
! [X1: $i] :
( $true
= ( ( func @ sK2 @ sK3 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( ap @ sK2 @ sK3 @ X1 @ Y0 )
= ( ap @ sK2 @ sK3 @ sK4 @ Y0 ) ) ) )
=> ( sK4 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( func @ sK2 @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( ap @ sK2 @ sK3 @ Y0 @ Y1 )
= ( ap @ sK2 @ sK3 @ sK4 @ Y1 ) ) ) )
=> ( sK4 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ sK2 @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( ap @ sK2 @ sK3 @ Y0 @ Y1 )
= ( ap @ sK2 @ sK3 @ sK4 @ Y1 ) ) ) )
=> ( sK4 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ sK2 @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( ap @ sK2 @ sK3 @ Y0 @ Y1 )
= ( ap @ sK2 @ sK3 @ sK4 @ Y1 ) ) ) )
=> ( sK4 = Y0 ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f123,f74]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( func @ X3 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ X3 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ( ap @ X3 @ X2 @ Y0 @ Y1 )
= ( ap @ X3 @ X2 @ X1 @ Y1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( func @ Y0 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y0 @ X2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( ap @ Y0 @ X2 @ Y1 @ Y2 )
= ( ap @ Y0 @ X2 @ X1 @ Y2 ) ) ) )
=> ( X1 = Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ Y0 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y0 @ X2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( ap @ Y0 @ X2 @ Y1 @ Y2 )
= ( ap @ Y0 @ X2 @ X1 @ Y2 ) ) ) )
=> ( X1 = Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f119]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= ( ap @ Y1 @ Y0 @ X1 @ Y3 ) ) ) )
=> ( X1 = Y2 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= ( ap @ Y1 @ Y0 @ X1 @ Y3 ) ) ) )
=> ( X1 = Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y3 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y0 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU696^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:31:25 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SEU696^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.46 % Domain : Set Theory
% 0.26/0.46 % Problem : Functions - Extensionality and Beta Reduction
% 0.26/0.46 % Version : Especial > Reduced > Especial.
% 0.26/0.46 % English : (! A:i.! B:i.! f:i.func A B f -> lam A B (^ x:i.ap A B f x) = f)
% 0.26/0.46
% 0.26/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.46 % Source : [Bro08]
% 0.26/0.46 % Names : ZFC198l [Bro08]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.33 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, 0.67 v3.7.0
% 0.26/0.46 % Syntax : Number of formulae : 15 ( 5 unt; 9 typ; 5 def)
% 0.26/0.46 % Number of atoms : 31 ( 10 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 6 ( 5 avg)
% 0.26/0.46 % Number of connectives : 85 ( 0 ~; 0 |; 0 &; 69 @)
% 0.26/0.46 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 12 ( 3 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 10 ( 9 usr; 4 con; 0-4 aty)
% 0.26/0.46 % Number of variables : 29 ( 8 ^; 21 !; 0 ?; 29 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : http://mathgate.info/detsetitem.php?id=402
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(in_type,type,
% 0.26/0.46 in: $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(dpsetconstr_type,type,
% 0.26/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.26/0.46
% 0.26/0.46 thf(func_type,type,
% 0.26/0.46 func: $i > $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(ap_type,type,
% 0.26/0.46 ap: $i > $i > $i > $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(app_type,type,
% 0.26/0.46 app: $o ).
% 0.26/0.46
% 0.26/0.46 thf(app,definition,
% 0.26/0.46 ( app
% 0.26/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.46 ( ( func @ A @ B @ Xf )
% 0.26/0.46 => ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(lam_type,type,
% 0.26/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.26/0.46
% 0.26/0.46 thf(lam,definition,
% 0.26/0.46 ( lam
% 0.26/0.46 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.46 ( dpsetconstr @ A @ B
% 0.26/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.26/0.46 ( ( Xf @ Xx )
% 0.26/0.46 = Xy ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(lamp_type,type,
% 0.26/0.46 lamp: $o ).
% 0.26/0.46
% 0.26/0.46 thf(lamp,definition,
% 0.26/0.46 ( lamp
% 0.26/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.46 ( ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.46 => ( func @ A @ B
% 0.26/0.46 @ ( lam @ A @ B
% 0.26/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(funcext_type,type,
% 0.26/0.46 funcext: $o ).
% 0.26/0.46
% 0.26/0.46 thf(funcext,definition,
% 0.26/0.46 ( funcext
% 0.26/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.46 ( ( func @ A @ B @ Xf )
% 0.26/0.46 => ! [Xg: $i] :
% 0.26/0.46 ( ( func @ A @ B @ Xg )
% 0.26/0.46 => ( ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.26/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.26/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(beta1_type,type,
% 0.26/0.46 beta1: $o ).
% 0.26/0.46
% 0.26/0.46 thf(beta1,definition,
% 0.26/0.46 ( beta1
% 0.26/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.46 ( ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.46 => ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( ( ap @ A @ B
% 0.26/0.46 @ ( lam @ A @ B
% 0.26/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.26/0.46 @ Xx )
% 0.26/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(eta1,conjecture,
% 0.26/0.46 ( app
% 0.26/0.46 => ( lamp
% 0.26/0.46 => ( funcext
% 0.26/0.46 => ( beta1
% 0.26/0.46 => ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.46 ( ( func @ A @ B @ Xf )
% 0.26/0.46 => ( ( lam @ A @ B
% 0.26/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.26/0.46 = Xf ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.51/1.29 ---- Embedded in THF ---
% 1.51/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.30 %%% Generated on Tue Feb 24 12:31:26 EST 2026
% 1.51/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.30 %%% Logic specification used:
% 1.51/1.30 %%% thf(spec, logic, $$dhol).
% 1.51/1.30
% 1.51/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2DTF14978.p
% See solution above
% 1.51/1.30 ------------------------
% 1.69/1.30 ---- Cleaned THF ---
% 1.69/1.31 thf(in_type,type,
% 1.69/1.31 in: $i > $i > $o ).
% 1.69/1.31
% 1.69/1.31 thf(dpsetconstr_type,type,
% 1.69/1.31 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.69/1.31
% 1.69/1.31 thf(func_type,type,
% 1.69/1.31 func: $i > $i > $i > $o ).
% 1.69/1.31
% 1.69/1.31 thf(ap_type,type,
% 1.69/1.31 ap: $i > $i > $i > $i > $i ).
% 1.69/1.31
% 1.69/1.31 thf(app_type,type,
% 1.69/1.31 app: $o ).
% 1.69/1.31
% 1.69/1.31 thf(app,definition,
% 1.69/1.31 ( app
% 1.69/1.31 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.69/1.31 ( ( func @ A @ B @ Xf )
% 1.69/1.31 => ! [Xx: $i] :
% 1.69/1.31 ( ( in @ Xx @ A )
% 1.69/1.31 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(lam_type,type,
% 1.69/1.31 lam: $i > $i > ( $i > $i ) > $i ).
% 1.69/1.31
% 1.69/1.31 thf(lam,definition,
% 1.69/1.31 ( lam
% 1.69/1.31 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 1.69/1.31 ( dpsetconstr @ A @ B
% 1.69/1.31 @ ^ [Xx: $i,Xy: $i] :
% 1.69/1.31 ( ( Xf @ Xx )
% 1.69/1.31 = Xy ) ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(lamp_type,type,
% 1.69/1.31 lamp: $o ).
% 1.69/1.31
% 1.69/1.31 thf(lamp,definition,
% 1.69/1.31 ( lamp
% 1.69/1.31 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 1.69/1.31 ( ! [Xx: $i] :
% 1.69/1.31 ( ( in @ Xx @ A )
% 1.69/1.31 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.69/1.31 => ( func @ A @ B
% 1.69/1.31 @ ( lam @ A @ B
% 1.69/1.31 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(funcext_type,type,
% 1.69/1.31 funcext: $o ).
% 1.69/1.31
% 1.69/1.31 thf(funcext,definition,
% 1.69/1.31 ( funcext
% 1.69/1.31 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.69/1.31 ( ( func @ A @ B @ Xf )
% 1.69/1.31 => ! [Xg: $i] :
% 1.69/1.31 ( ( func @ A @ B @ Xg )
% 1.69/1.31 => ( ! [Xx: $i] :
% 1.69/1.31 ( ( in @ Xx @ A )
% 1.69/1.31 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.69/1.31 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 1.69/1.31 => ( Xf = Xg ) ) ) ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(beta1_type,type,
% 1.69/1.31 beta1: $o ).
% 1.69/1.31
% 1.69/1.31 thf(beta1,definition,
% 1.69/1.31 ( beta1
% 1.69/1.31 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 1.69/1.31 ( ! [Xx: $i] :
% 1.69/1.31 ( ( in @ Xx @ A )
% 1.69/1.31 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.69/1.31 => ! [Xx: $i] :
% 1.69/1.31 ( ( in @ Xx @ A )
% 1.69/1.31 => ( ( ap @ A @ B
% 1.69/1.31 @ ( lam @ A @ B
% 1.69/1.31 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 1.69/1.31 @ Xx )
% 1.69/1.31 = ( Xf @ Xx ) ) ) ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(eta1,conjecture,
% 1.69/1.31 ( app
% 1.69/1.31 => ( lamp
% 1.69/1.31 => ( funcext
% 1.69/1.31 => ( beta1
% 1.69/1.31 => ! [A: $i,B: $i,Xf: $i] :
% 1.69/1.31 ( ( func @ A @ B @ Xf )
% 1.69/1.31 => ( ( lam @ A @ B
% 1.69/1.31 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 1.69/1.31 = Xf ) ) ) ) ) ) ).
% 1.69/1.31 ------------------------
% 1.69/1.32 % (15249)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_14978 for (2999ds/4Mi)
% 1.69/1.32 % (15248)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/183Mi)
% 1.69/1.32 % (15249)Instruction limit reached!
% 1.69/1.32 % (15249)------------------------------
% 1.69/1.32 % (15249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (15249)Termination reason: Unknown
% 1.69/1.32 % (15249)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (15249)Memory used [KB]: 5500
% 1.69/1.32 % (15249)Time elapsed: 0.003 s
% 1.69/1.32 % (15249)Instructions burned: 5 (million)
% 1.69/1.32 % (15249)------------------------------
% 1.69/1.32 % (15249)------------------------------
% 1.69/1.33 % (15250)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_14978 for (2999ds/27Mi)
% 1.69/1.33 % (15251)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/2Mi)
% 1.69/1.33 % (15252)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_14978 for (2999ds/2Mi)
% 1.69/1.33 % (15254)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/18Mi)
% 1.69/1.33 % (15253)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_14978 for (2999ds/275Mi)
% 1.69/1.33 % (15251)Instruction limit reached!
% 1.69/1.33 % (15251)------------------------------
% 1.69/1.33 % (15251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (15251)Termination reason: Unknown
% 1.69/1.33 % (15251)Termination phase: shuffling
% 1.69/1.33
% 1.69/1.33 % (15251)Memory used [KB]: 895
% 1.69/1.33 % (15251)Time elapsed: 0.003 s
% 1.69/1.33 % (15251)Instructions burned: 2 (million)
% 1.69/1.33 % (15251)------------------------------
% 1.69/1.33 % (15251)------------------------------
% 1.69/1.33 % (15252)Instruction limit reached!
% 1.69/1.33 % (15252)------------------------------
% 1.69/1.33 % (15252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (15252)Termination reason: Unknown
% 1.69/1.33 % (15252)Termination phase: shuffling
% 1.69/1.33
% 1.69/1.33 % (15252)Memory used [KB]: 895
% 1.69/1.33 % (15252)Time elapsed: 0.003 s
% 1.69/1.33 % (15252)Instructions burned: 2 (million)
% 1.69/1.33 % (15252)------------------------------
% 1.69/1.33 % (15252)------------------------------
% 1.69/1.33 % (15255)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/3Mi)
% 1.69/1.33 % (15255)Instruction limit reached!
% 1.69/1.33 % (15255)------------------------------
% 1.69/1.33 % (15255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (15255)Termination reason: Unknown
% 1.69/1.33 % (15255)Termination phase: Property scanning
% 1.69/1.33
% 1.69/1.33 % (15255)Memory used [KB]: 1023
% 1.69/1.33 % (15255)Time elapsed: 0.002 s
% 1.69/1.33 % (15255)Instructions burned: 4 (million)
% 1.69/1.33 % (15255)------------------------------
% 1.69/1.33 % (15255)------------------------------
% 1.69/1.34 % (15254)Instruction limit reached!
% 1.69/1.34 % (15254)------------------------------
% 1.69/1.34 % (15254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (15254)Termination reason: Unknown
% 1.69/1.34 % (15254)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (15254)Memory used [KB]: 5628
% 1.69/1.34 % (15254)Time elapsed: 0.014 s
% 1.69/1.34 % (15254)Instructions burned: 19 (million)
% 1.69/1.34 % (15254)------------------------------
% 1.69/1.34 % (15254)------------------------------
% 1.69/1.34 % (15258)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_14978 for (2999ds/3Mi)
% 1.69/1.34 % (15258)Instruction limit reached!
% 1.69/1.34 % (15258)------------------------------
% 1.69/1.34 % (15258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (15258)Termination reason: Unknown
% 1.69/1.34 % (15258)Termination phase: Property scanning
% 1.69/1.34
% 1.69/1.34 % (15258)Memory used [KB]: 1023
% 1.69/1.34 % (15258)Time elapsed: 0.002 s
% 1.69/1.34 % (15258)Instructions burned: 4 (million)
% 1.69/1.34 % (15258)------------------------------
% 1.69/1.34 % (15258)------------------------------
% 1.69/1.34 % (15250)Instruction limit reached!
% 1.69/1.34 % (15250)------------------------------
% 1.69/1.34 % (15250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (15250)Termination reason: Unknown
% 1.69/1.34 % (15250)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (15250)Memory used [KB]: 5628
% 1.69/1.34 % (15250)Time elapsed: 0.018 s
% 1.69/1.34 % (15250)Instructions burned: 27 (million)
% 1.69/1.34 % (15250)------------------------------
% 1.69/1.34 % (15250)------------------------------
% 1.69/1.35 % (15256)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_14978 for (2999ds/37Mi)
% 1.69/1.35 % (15257)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_14978 for (2999ds/15Mi)
% 1.69/1.35 % (15260)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/7Mi)
% 1.69/1.35 % (15260)Instruction limit reached!
% 1.69/1.35 % (15260)------------------------------
% 1.69/1.35 % (15260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (15260)Termination reason: Unknown
% 1.69/1.35 % (15260)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (15260)Memory used [KB]: 1023
% 1.69/1.35 % (15260)Time elapsed: 0.003 s
% 1.69/1.35 % (15260)Instructions burned: 7 (million)
% 1.69/1.35 % (15260)------------------------------
% 1.69/1.35 % (15260)------------------------------
% 1.69/1.36 % (15257)Instruction limit reached!
% 1.69/1.36 % (15257)------------------------------
% 1.69/1.36 % (15257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (15257)Termination reason: Unknown
% 1.69/1.36 % (15257)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (15257)Memory used [KB]: 5756
% 1.69/1.36 % (15257)Time elapsed: 0.012 s
% 1.69/1.36 % (15257)Instructions burned: 16 (million)
% 1.69/1.36 % (15257)------------------------------
% 1.69/1.36 % (15257)------------------------------
% 1.69/1.36 % (15259)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_14978 for (2999ds/1041Mi)
% 1.69/1.36 % (15261)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/16Mi)
% 1.69/1.36 % (15262)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_14978 for (2999ds/3Mi)
% 1.69/1.36 % (15262)Instruction limit reached!
% 1.69/1.36 % (15262)------------------------------
% 1.69/1.36 % (15262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (15262)Termination reason: Unknown
% 1.69/1.36 % (15262)Termination phase: Preprocessing 3
% 1.69/1.36
% 1.69/1.36 % (15262)Memory used [KB]: 1023
% 1.69/1.36 % (15262)Time elapsed: 0.002 s
% 1.69/1.36 % (15262)Instructions burned: 4 (million)
% 1.69/1.36 % (15262)------------------------------
% 1.69/1.36 % (15262)------------------------------
% 1.69/1.37 % (15256)Instruction limit reached!
% 1.69/1.37 % (15256)------------------------------
% 1.69/1.37 % (15256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (15256)Termination reason: Unknown
% 1.69/1.37 % (15256)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (15256)Memory used [KB]: 5756
% 1.69/1.37 % (15256)Time elapsed: 0.023 s
% 1.69/1.37 % (15256)Instructions burned: 37 (million)
% 1.69/1.37 % (15256)------------------------------
% 1.69/1.37 % (15256)------------------------------
% 1.69/1.37 % (15261)Instruction limit reached!
% 1.69/1.37 % (15261)------------------------------
% 1.69/1.37 % (15261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (15261)Termination reason: Unknown
% 1.69/1.37 % (15261)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (15261)Memory used [KB]: 6012
% 1.69/1.37 % (15261)Time elapsed: 0.012 s
% 1.69/1.37 % (15261)Instructions burned: 16 (million)
% 1.69/1.37 % (15261)------------------------------
% 1.69/1.37 % (15261)------------------------------
% 1.69/1.37 % (15264)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/7Mi)
% 1.69/1.37 % (15263)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_14978 for (2999ds/3Mi)
% 1.69/1.38 % (15264)Instruction limit reached!
% 1.69/1.38 % (15264)------------------------------
% 1.69/1.38 % (15264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (15264)Termination reason: Unknown
% 1.69/1.38 % (15264)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (15264)Memory used [KB]: 5500
% 1.69/1.38 % (15264)Time elapsed: 0.003 s
% 1.69/1.38 % (15264)Instructions burned: 7 (million)
% 1.69/1.38 % (15264)------------------------------
% 1.69/1.38 % (15264)------------------------------
% 1.69/1.38 % (15263)Instruction limit reached!
% 1.69/1.38 % (15263)------------------------------
% 1.69/1.38 % (15263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (15263)Termination reason: Unknown
% 1.69/1.38 % (15263)Termination phase: Property scanning
% 1.69/1.38
% 1.69/1.38 % (15263)Memory used [KB]: 1023
% 1.69/1.38 % (15263)Time elapsed: 0.004 s
% 1.69/1.38 % (15263)Instructions burned: 4 (million)
% 1.69/1.38 % (15263)------------------------------
% 1.69/1.38 % (15263)------------------------------
% 1.69/1.38 % (15248)Instruction limit reached!
% 1.69/1.38 % (15248)------------------------------
% 1.69/1.38 % (15248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (15248)Termination reason: Unknown
% 1.69/1.38 % (15248)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (15248)Memory used [KB]: 6140
% 1.69/1.38 % (15248)Time elapsed: 0.058 s
% 1.69/1.38 % (15248)Instructions burned: 183 (million)
% 1.69/1.38 % (15248)------------------------------
% 1.69/1.38 % (15248)------------------------------
% 1.69/1.38 % (15259)First to succeed.
% 1.69/1.38 % (15267)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/18Mi)
% 1.69/1.38 % (15265)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/3Mi)
% 1.69/1.39 % (15265)Instruction limit reached!
% 1.69/1.39 % (15265)------------------------------
% 1.69/1.39 % (15265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (15265)Termination reason: Unknown
% 1.69/1.39 % (15265)Termination phase: Function definition elimination
% 1.69/1.39
% 1.69/1.39 % (15265)Memory used [KB]: 1023
% 1.69/1.39 % (15265)Time elapsed: 0.004 s
% 1.69/1.39 % (15265)Instructions burned: 4 (million)
% 1.69/1.39 % (15265)------------------------------
% 1.69/1.39 % (15265)------------------------------
% 1.69/1.39 % (15269)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14978 for (2999ds/6Mi)
% 1.69/1.39 % (15259)Refutation found. Thanks to Tanya!
% 1.69/1.39 % SZS status Theorem for DTF2THF_14978
% 1.69/1.39 % SZS output start Proof for DTF2THF_14978
% 1.69/1.39 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.39 thf(func_def_1, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.69/1.39 thf(func_def_2, type, func: $i > $i > $i > $o).
% 1.69/1.39 thf(func_def_3, type, ap: $i > $i > $i > $i > $i).
% 1.69/1.39 thf(func_def_6, type, lam: $i > $i > ($i > $i) > $i).
% 1.69/1.39 thf(func_def_24, type, ph1: !>[X0: $tType]:(X0)).
% 1.69/1.39 thf(f154,plain,(
% 1.69/1.39 $false),
% 1.69/1.39 inference(subsumption_resolution,[status(thm)],[f150,f79])).
% 1.69/1.39 thf(f79,plain,(
% 1.69/1.39 ((dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0)))) != sK4)),
% 1.69/1.39 inference(equality_proxy_clausification,[status(thm)],[f76])).
% 1.69/1.39 thf(f76,plain,(
% 1.69/1.39 ($false = ((dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0)))) = sK4))),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f75])).
% 1.69/1.39 thf(f75,plain,(
% 1.69/1.39 (($true => ((dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0)))) = sK4)) = $false)),
% 1.69/1.39 inference(backward_demodulation,[status(thm)],[f72,f74])).
% 1.69/1.39 thf(f74,plain,(
% 1.69/1.39 ((func @ sK2 @ sK3 @ sK4) = $true)),
% 1.69/1.39 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.69/1.39 thf(f72,plain,(
% 1.69/1.39 ($false = ((func @ sK2 @ sK3 @ sK4) => ((dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0)))) = sK4)))),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.69/1.39 thf(f71,plain,(
% 1.69/1.39 (((^[Y0 : $i]: ((func @ sK2 @ sK3 @ Y0) => ((dpsetconstr @ sK2 @ sK3 @ (^[Y1 : $i]: (= @ (ap @ sK2 @ sK3 @ Y0 @ Y1)))) = Y0))) @ sK4) = $false)),
% 1.69/1.39 inference(sigma_clausification,[status(thm)],[f70])).
% 1.69/1.39 thf(f70,plain,(
% 1.69/1.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((func @ sK2 @ sK3 @ Y0) => ((dpsetconstr @ sK2 @ sK3 @ (^[Y1 : $i]: (= @ (ap @ sK2 @ sK3 @ Y0 @ Y1)))) = Y0)))))),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.69/1.39 thf(f69,plain,(
% 1.69/1.39 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ sK2 @ Y0 @ Y1) => ((dpsetconstr @ sK2 @ Y0 @ (^[Y2 : $i]: (= @ (ap @ sK2 @ Y0 @ Y1 @ Y2)))) = Y1))))) @ sK3))),
% 1.69/1.39 inference(sigma_clausification,[status(thm)],[f68])).
% 1.69/1.39 thf(f68,plain,(
% 1.69/1.39 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ sK2 @ Y0 @ Y1) => ((dpsetconstr @ sK2 @ Y0 @ (^[Y2 : $i]: (= @ (ap @ sK2 @ Y0 @ Y1 @ Y2)))) = Y1)))))))),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.69/1.39 thf(f67,plain,(
% 1.69/1.39 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2))))))) @ sK2) = $false)),
% 1.69/1.39 inference(sigma_clausification,[status(thm)],[f66])).
% 1.69/1.39 thf(f66,plain,(
% 1.69/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2)))))))) = $false)),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f65])).
% 1.69/1.39 thf(f65,plain,(
% 1.69/1.39 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2))))))))))),
% 1.69/1.39 inference(backward_demodulation,[status(thm)],[f62,f64])).
% 1.69/1.39 thf(f64,plain,(
% 1.69/1.39 ($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) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3) = (Y2 @ Y3)))))))))))))),
% 1.69/1.39 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.69/1.39 thf(f62,plain,(
% 1.69/1.39 (((!! @ $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) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3) = (Y2 @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2))))))))) = $false)),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f61])).
% 1.69/1.39 thf(f61,plain,(
% 1.69/1.39 ($false = ($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) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3) = (Y2 @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2)))))))))))),
% 1.69/1.39 inference(backward_demodulation,[status(thm)],[f46,f60])).
% 1.69/1.39 thf(f60,plain,(
% 1.69/1.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))))),
% 1.69/1.39 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.69/1.39 thf(f46,plain,(
% 1.69/1.39 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = 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) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3) = (Y2 @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2)))))))))))),
% 1.69/1.39 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.69/1.39 thf(f33,plain,(
% 1.69/1.39 ($false = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = 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) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3) = (Y2 @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2))))))))))))),
% 1.69/1.39 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.69/1.39 thf(f30,plain,(
% 1.69/1.39 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = 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) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3) = (Y2 @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2)))))))))))) = $false)),
% 1.69/1.39 inference(not_proxy_clausification,[status(thm)],[f29])).
% 1.69/1.39 thf(f29,plain,(
% 1.69/1.39 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = 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) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3) = (Y2 @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (ap @ Y0 @ Y1 @ Y2 @ Y3)))) = Y2))))))))))))) = $true)),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.69/1.39 thf(f28,plain,(
% 1.69/1.39 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = 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) => ((ap @ Y0 @ Y1 @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i > $i]: (dpsetconstr @ Y4 @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $i]: ((Y6 @ Y7) = Y8)))))))))) @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3) = (Y2 @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y0 @ Y1 @ (^[Y3 : $i]: (ap @ Y0 @ Y1 @ Y2 @ Y3))) = Y2))))))))))))) = $true)),
% 1.69/1.39 inference(definition_unfolding,[status(thm)],[f22,f24,f26,f25,f27,f21])).
% 1.69/1.39 thf(f21,plain,(
% 1.69/1.39 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 1.69/1.39 inference(cnf_transformation,[status(thm)],[f13])).
% 1.69/1.39 thf(f13,plain,(
% 1.69/1.39 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 1.69/1.39 inference(fool_elimination,[status(thm)],[f2])).
% 1.69/1.39 thf(f2,axiom,(
% 1.69/1.39 (lam = (^[X0 : $i, X1 : $i, X2 : $i > $i] : (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : (((X2 @ X3) = X4))))))),
% 1.69/1.39 file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',lam)).
% 1.69/1.39 thf(f27,plain,(
% 1.69/1.39 (beta1 = (!! @ $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) => ((ap @ Y0 @ Y1 @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i > $i]: (dpsetconstr @ Y4 @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $i]: ((Y6 @ Y7) = Y8)))))))))) @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3) = (Y2 @ Y3)))))))))))))),
% 1.69/1.39 inference(definition_unfolding,[status(thm)],[f20,f21])).
% 1.69/1.39 thf(f20,plain,(
% 1.69/1.39 (beta1 = (!! @ $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) => ((ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3) = (Y2 @ Y3)))))))))))))),
% 1.69/1.39 inference(cnf_transformation,[status(thm)],[f19])).
% 1.69/1.39 thf(f19,plain,(
% 1.69/1.39 (beta1 = (!! @ $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) => ((ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3) = (Y2 @ Y3)))))))))))))),
% 1.69/1.39 inference(fool_elimination,[status(thm)],[f18])).
% 1.69/1.39 thf(f18,plain,(
% 1.69/1.39 (! [X0 : $i > $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => ! [X4 : $i] : ((in @ X4 @ X2) => ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[X5 : $i] : (X0 @ X5))) @ X4) = (X0 @ X4)))) = beta1)),
% 1.69/1.39 inference(rectify,[status(thm)],[f5])).
% 1.69/1.39 thf(f5,axiom,(
% 1.69/1.39 (! [X2 : $i > $i,X1 : $i,X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : (X2 @ X4))) @ X3) = (X2 @ X3)))) = beta1)),
% 1.69/1.39 file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',beta1)).
% 1.69/1.39 thf(f25,plain,(
% 1.69/1.39 (funcext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))))),
% 1.69/1.39 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.39 thf(f17,plain,(
% 1.69/1.39 (funcext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))))),
% 1.69/1.39 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.39 thf(f16,plain,(
% 1.69/1.39 (funcext = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((func @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ((ap @ X0 @ X1 @ X3 @ X4) = (ap @ X0 @ X1 @ X2 @ X4))) => (X2 = X3)))))),
% 1.69/1.39 inference(rectify,[status(thm)],[f4])).
% 1.69/1.39 thf(f4,axiom,(
% 1.69/1.39 (funcext = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X5 : $i] : ((func @ X0 @ X1 @ X5) => (! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ X2 @ X3) = (ap @ X0 @ X1 @ X5 @ X3))) => (X2 = X5)))))),
% 1.69/1.39 file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',funcext)).
% 1.69/1.39 thf(f26,plain,(
% 1.69/1.39 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 1.69/1.39 inference(definition_unfolding,[status(thm)],[f23,f21])).
% 1.69/1.39 thf(f23,plain,(
% 1.69/1.39 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (lam @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 1.69/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.69/1.39 thf(f12,plain,(
% 1.69/1.39 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (lam @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 1.69/1.39 inference(fool_elimination,[status(thm)],[f11])).
% 1.69/1.39 thf(f11,plain,(
% 1.69/1.39 (lamp = ! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X2 @ X3) @ X0)) => (func @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[X4 : $i] : (X2 @ X4))))))),
% 1.69/1.39 inference(rectify,[status(thm)],[f3])).
% 1.69/1.39 thf(f3,axiom,(
% 1.69/1.39 (lamp = ! [X1 : $i,X0 : $i,X2 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : (X2 @ X3))))))),
% 1.69/1.39 file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',lamp)).
% 1.69/1.39 thf(f24,plain,(
% 1.69/1.39 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))))),
% 1.69/1.39 inference(cnf_transformation,[status(thm)],[f15])).
% 1.69/1.39 thf(f15,plain,(
% 1.69/1.39 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))))),
% 1.69/1.39 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.39 thf(f14,plain,(
% 1.69/1.39 (app = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (ap @ X2 @ X0 @ X1 @ X3) @ X0))))),
% 1.69/1.39 inference(rectify,[status(thm)],[f1])).
% 1.69/1.39 thf(f1,axiom,(
% 1.69/1.39 (app = ! [X1 : $i,X2 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))))),
% 1.69/1.39 file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',app)).
% 1.69/1.39 thf(f22,plain,(
% 1.69/1.39 ((~ (app => (lamp => (funcext => (beta1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((lam @ Y0 @ Y1 @ (^[Y3 : $i]: (ap @ Y0 @ Y1 @ Y2 @ Y3))) = Y2))))))))))))) = $true)),
% 1.69/1.39 inference(cnf_transformation,[status(thm)],[f10])).
% 1.69/1.39 thf(f10,plain,(
% 1.69/1.39 ((~ (app => (lamp => (funcext => (beta1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((lam @ Y0 @ Y1 @ (^[Y3 : $i]: (ap @ Y0 @ Y1 @ Y2 @ Y3))) = Y2))))))))))))) = $true)),
% 1.69/1.39 inference(fool_elimination,[status(thm)],[f9])).
% 1.69/1.39 thf(f9,plain,(
% 1.69/1.39 ~(app => (lamp => (funcext => (beta1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => ((lam @ X2 @ X1 @ (^[X3 : $i] : (ap @ X2 @ X1 @ X0 @ X3))) = X0))))))),
% 1.69/1.39 inference(rectify,[status(thm)],[f7])).
% 1.69/1.39 thf(f7,negated_conjecture,(
% 1.69/1.39 ~(app => (lamp => (funcext => (beta1 => ! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ((lam @ X0 @ X1 @ (^[X3 : $i] : (ap @ X0 @ X1 @ X2 @ X3))) = X2))))))),
% 1.69/1.39 inference(negated_conjecture,[status(cth)],[f6])).
% 1.69/1.39 thf(f6,conjecture,(
% 1.69/1.39 app => (lamp => (funcext => (beta1 => ! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ((lam @ X0 @ X1 @ (^[X3 : $i] : (ap @ X0 @ X1 @ X2 @ X3))) = X2)))))),
% 1.69/1.39 file('/export/starexec/sandbox2/tmp/tmp.KIbRWNnxJQ/DTF2THF_14978.p',eta1)).
% 1.69/1.39 thf(f150,plain,(
% 1.69/1.39 ((dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0)))) = sK4)),
% 1.69/1.39 inference(equality_proxy_clausification,[status(thm)],[f147])).
% 1.69/1.39 thf(f147,plain,(
% 1.69/1.39 ($true = (sK4 = (dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0))))))),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f146])).
% 1.69/1.39 thf(f146,plain,(
% 1.69/1.39 (($true => (sK4 = (dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0)))))) = $true)),
% 1.69/1.39 inference(forward_demodulation,[status(thm)],[f141,f83])).
% 1.69/1.39 thf(f83,plain,(
% 1.69/1.39 ($true = (func @ sK2 @ sK3 @ (dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0))))))),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f82])).
% 1.69/1.39 thf(f82,plain,(
% 1.69/1.39 ($true = ($true => (func @ sK2 @ sK3 @ (dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0)))))))),
% 1.69/1.39 inference(superposition,[status(thm)],[f57,f78])).
% 1.69/1.39 thf(f78,plain,(
% 1.69/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (in @ (ap @ sK2 @ sK3 @ sK4 @ Y0) @ sK3)))) = $true)),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f77])).
% 1.69/1.39 thf(f77,plain,(
% 1.69/1.39 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (in @ (ap @ sK2 @ sK3 @ sK4 @ Y0) @ sK3))))) = $true)),
% 1.69/1.39 inference(superposition,[status(thm)],[f44,f74])).
% 1.69/1.39 thf(f44,plain,(
% 1.69/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((func @ X1 @ X3 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (ap @ X1 @ X3 @ X2 @ Y0) @ X3))))))) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.69/1.39 thf(f43,plain,(
% 1.69/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((func @ X1 @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (ap @ X1 @ Y0 @ X2 @ Y1) @ Y0)))))) @ X3) = $true)) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f42])).
% 1.69/1.39 thf(f42,plain,(
% 1.69/1.39 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((func @ X1 @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (ap @ X1 @ Y0 @ X2 @ Y1) @ Y0))))))) = $true)) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.69/1.39 thf(f41,plain,(
% 1.69/1.39 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (ap @ X1 @ Y1 @ Y0 @ Y2) @ Y1)))))))) @ X2))) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f40])).
% 1.69/1.39 thf(f40,plain,(
% 1.69/1.39 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (ap @ X1 @ Y1 @ Y0 @ Y2) @ Y1))))))))))) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.69/1.39 thf(f39,plain,(
% 1.69/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2)))))))))) @ X1) = $true)) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f34])).
% 1.69/1.39 thf(f34,plain,(
% 1.69/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) = $true)),
% 1.69/1.39 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.69/1.39 thf(f57,plain,(
% 1.69/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (X1 @ Y0) @ X3)))) => (func @ X2 @ X3 @ (dpsetconstr @ X2 @ X3 @ (^[Y0 : $i]: (= @ (X1 @ Y0)))))) = $true)) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.69/1.39 thf(f56,plain,(
% 1.69/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (X1 @ Y1) @ Y0)))) => (func @ X2 @ Y0 @ (dpsetconstr @ X2 @ Y0 @ (^[Y1 : $i]: (= @ (X1 @ Y1))))))) @ X3))) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f55])).
% 1.69/1.39 thf(f55,plain,(
% 1.69/1.39 ( ! [X2 : $i,X1 : $i > $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (X1 @ Y1) @ Y0)))) => (func @ X2 @ Y0 @ (dpsetconstr @ X2 @ Y0 @ (^[Y1 : $i]: (= @ (X1 @ Y1)))))))))) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.69/1.39 thf(f54,plain,(
% 1.69/1.39 ( ! [X2 : $i,X1 : $i > $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (X1 @ Y2) @ Y1)))) => (func @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y2 : $i]: (= @ (X1 @ Y2))))))))) @ X2) = $true)) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f53])).
% 1.69/1.39 thf(f53,plain,(
% 1.69/1.39 ( ! [X1 : $i > $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (X1 @ Y2) @ Y1)))) => (func @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y2 : $i]: (= @ (X1 @ Y2)))))))))) = $true)) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.69/1.39 thf(f52,plain,(
% 1.69/1.39 ( ! [X1 : $i > $i] : (($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3))))))))))) @ X1))) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f47])).
% 1.69/1.39 thf(f47,plain,(
% 1.69/1.39 ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) = $true)),
% 1.69/1.39 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.69/1.39 thf(f141,plain,(
% 1.69/1.39 (((func @ sK2 @ sK3 @ (dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0))))) => (sK4 = (dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0)))))) = $true)),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f136])).
% 1.69/1.39 thf(f136,plain,(
% 1.69/1.39 ($true = ((func @ sK2 @ sK3 @ (dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0))))) => ($true => (sK4 = (dpsetconstr @ sK2 @ sK3 @ (^[Y0 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y0))))))))),
% 1.69/1.39 inference(superposition,[status(thm)],[f133,f107])).
% 1.69/1.39 thf(f107,plain,(
% 1.69/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((ap @ sK2 @ sK3 @ (dpsetconstr @ sK2 @ sK3 @ (^[Y1 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y1)))) @ Y0) = (ap @ sK2 @ sK3 @ sK4 @ Y0))))) = $true)),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f105])).
% 1.69/1.39 thf(f105,plain,(
% 1.69/1.39 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((ap @ sK2 @ sK3 @ (dpsetconstr @ sK2 @ sK3 @ (^[Y1 : $i]: (= @ (ap @ sK2 @ sK3 @ sK4 @ Y1)))) @ Y0) = (ap @ sK2 @ sK3 @ sK4 @ Y0)))))) = $true)),
% 1.69/1.39 inference(superposition,[status(thm)],[f102,f78])).
% 1.69/1.39 thf(f102,plain,(
% 1.69/1.39 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (X3 @ Y0) @ X2)))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((ap @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y1 : $i]: (= @ (X3 @ Y1)))) @ Y0) = (X3 @ Y0)))))) = $true)) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.69/1.39 thf(f101,plain,(
% 1.69/1.39 ( ! [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) => ((ap @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y2 : $i]: (= @ (Y0 @ Y2)))) @ Y1) = (Y0 @ Y1))))))) @ X3))) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f94])).
% 1.69/1.39 thf(f94,plain,(
% 1.69/1.39 ( ! [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) => ((ap @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y2 : $i]: (= @ (Y0 @ Y2)))) @ Y1) = (Y0 @ Y1)))))))))) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.69/1.39 thf(f93,plain,(
% 1.69/1.39 ( ! [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) => ((ap @ X1 @ Y0 @ (dpsetconstr @ X1 @ Y0 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ Y2) = (Y1 @ Y2))))))))) @ X2))) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f88])).
% 1.69/1.39 thf(f88,plain,(
% 1.69/1.39 ( ! [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) => ((ap @ X1 @ Y0 @ (dpsetconstr @ X1 @ Y0 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ Y2) = (Y1 @ Y2)))))))))))) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f87])).
% 1.69/1.39 thf(f87,plain,(
% 1.69/1.39 ( ! [X1 : $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) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3) = (Y2 @ Y3))))))))))) @ X1) = $true)) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f64])).
% 1.69/1.39 thf(f133,plain,(
% 1.69/1.39 ( ! [X1 : $i] : (($true = ((func @ sK2 @ sK3 @ X1) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((ap @ sK2 @ sK3 @ X1 @ Y0) = (ap @ sK2 @ sK3 @ sK4 @ Y0))))) => (sK4 = X1))))) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.69/1.39 thf(f131,plain,(
% 1.69/1.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((func @ sK2 @ sK3 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((ap @ sK2 @ sK3 @ Y0 @ Y1) = (ap @ sK2 @ sK3 @ sK4 @ Y1))))) => (sK4 = Y0)))) @ X1))) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f128])).
% 1.69/1.39 thf(f128,plain,(
% 1.69/1.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((func @ sK2 @ sK3 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((ap @ sK2 @ sK3 @ Y0 @ Y1) = (ap @ sK2 @ sK3 @ sK4 @ Y1))))) => (sK4 = Y0))))))),
% 1.69/1.39 inference(boolean_simplification,[status(thm)],[f125])).
% 1.69/1.39 thf(f125,plain,(
% 1.69/1.39 (($true => (!! @ $i @ (^[Y0 : $i]: ((func @ sK2 @ sK3 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((ap @ sK2 @ sK3 @ Y0 @ Y1) = (ap @ sK2 @ sK3 @ sK4 @ Y1))))) => (sK4 = Y0)))))) = $true)),
% 1.69/1.39 inference(superposition,[status(thm)],[f123,f74])).
% 1.69/1.39 thf(f123,plain,(
% 1.69/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((func @ X3 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((func @ X3 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((ap @ X3 @ X2 @ Y0 @ Y1) = (ap @ X3 @ X2 @ X1 @ Y1))))) => (X1 = Y0)))))))) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f122])).
% 1.69/1.39 thf(f122,plain,(
% 1.69/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((func @ Y0 @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((func @ Y0 @ X2 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((ap @ Y0 @ X2 @ Y1 @ Y2) = (ap @ Y0 @ X2 @ X1 @ Y2))))) => (X1 = Y1))))))) @ X3))) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f120])).
% 1.69/1.39 thf(f120,plain,(
% 1.69/1.39 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((func @ Y0 @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((func @ Y0 @ X2 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((ap @ Y0 @ X2 @ Y1 @ Y2) = (ap @ Y0 @ X2 @ X1 @ Y2))))) => (X1 = Y1)))))))))) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f119])).
% 1.69/1.39 thf(f119,plain,(
% 1.69/1.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y1 @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = (ap @ Y1 @ Y0 @ X1 @ Y3))))) => (X1 = Y2))))))))) @ X2) = $true)) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f114])).
% 1.69/1.39 thf(f114,plain,(
% 1.69/1.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y1 @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = (ap @ Y1 @ Y0 @ X1 @ Y3))))) => (X1 = Y2)))))))))) = $true)) )),
% 1.69/1.39 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.69/1.39 thf(f113,plain,(
% 1.69/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((ap @ Y2 @ Y1 @ Y3 @ Y4) = (ap @ Y2 @ Y1 @ Y0 @ Y4))))) => (Y0 = Y3))))))))))) @ X1) = $true)) )),
% 1.69/1.39 inference(pi_clausification,[status(thm)],[f60])).
% 1.69/1.39 % SZS output end Proof for DTF2THF_14978
% 1.69/1.39 % (15259)------------------------------
% 1.69/1.39 % (15259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (15259)Termination reason: Refutation
% 1.69/1.39
% 1.69/1.39 % (15259)Memory used [KB]: 6012
% 1.69/1.39 % (15259)Time elapsed: 0.031 s
% 1.69/1.39 % (15259)Instructions burned: 69 (million)
% 1.69/1.39 % (15259)------------------------------
% 1.69/1.39 % (15259)------------------------------
% 1.69/1.39 % (15247)Success in time 0.07 s
%------------------------------------------------------------------------------