%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU558^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 09:35:16 AM UTC 2026
% Result : Theorem 1.63s 1.48s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 7
% Syntax : Number of formulae : 142 ( 75 unt; 0 typ; 2 def)
% Number of atoms : 1324 ( 274 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 2221 ( 87 ~; 64 |; 0 &;1458 @)
% ( 5 <=>; 356 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 154 ( 154 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 13 con; 0-2 aty)
% ( 251 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 397 ( 298 ^; 99 !; 0 ?; 397 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
sK4: $i > $o ).
thf(func_def_25,type,
sK5: $i > $o ).
thf(f1697,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f177,f968,f1696]) ).
thf(f1696,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f1695]) ).
thf(f1695,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f1694]) ).
thf(f1694,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1693]) ).
thf(f1693,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1683,f987]) ).
thf(f987,plain,
( ( ( sK5 @ sK7 )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f986]) ).
thf(f986,plain,
( ( ( sK5 @ sK7 )
= $true )
| ( $false = $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f984]) ).
thf(f984,plain,
( ( $false
= ( $false
=> ( in @ sK7 @ ( dsetconstr @ sK2 @ sK4 ) ) ) )
| ( ( sK5 @ sK7 )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f980,f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
=> ( X1 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( X1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1 @ Y2 )
= ( dsetconstr @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f43]) ).
thf(f43,plain,
( $false
= ( $true
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1 @ Y2 )
= ( dsetconstr @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f28,f42]) ).
thf(f42,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1 @ Y2 )
= ( dsetconstr @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1 @ Y2 )
= ( dsetconstr @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1 @ Y2 )
= ( dsetconstr @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f18,f19,f21,f22]) ).
thf(f22,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X0 ) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( setext
= ( ! [X0: $i,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',setext) ).
thf(f21,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( dsetconstrER
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',dsetconstrER) ).
thf(f19,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( dsetconstrEL
= ( ! [X2: $i,X1: $i > $o,X0: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',dsetconstrEL) ).
thf(f18,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( dsetconstrI
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',dsetconstrI) ).
thf(f20,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( X4 = X5 )
=> ( ( X3 @ X4 )
<=> ( X2 @ X5 ) ) ) ) )
=> ( ( dsetconstr @ X0
@ ^ [X6: $i] : ( X3 @ X6 ) )
= ( dsetconstr @ X1
@ ^ [X7: $i] : ( X2 @ X7 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ! [X0: $i,X4: $i] :
( ( X0 = X4 )
=> ! [X5: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X5 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X4
@ ^ [X2: $i] : ( X5 @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ! [X0: $i,X4: $i] :
( ( X0 = X4 )
=> ! [X5: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X5 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X4
@ ^ [X2: $i] : ( X5 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',dsetconstr__Cong) ).
thf(f980,plain,
( ( $false
= ( ( in @ sK7 @ ( dsetconstr @ sK2 @ sK5 ) )
=> ( in @ sK7 @ ( dsetconstr @ sK2 @ sK4 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f974]) ).
thf(f974,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) ) )
@ sK7 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f971]) ).
thf(f971,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f172]) ).
thf(f172,definition,
( spl0_1
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f1683,plain,
( ( ( ~ ( sK5 @ sK7 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1682]) ).
thf(f1682,plain,
( ( $true
= ( $true
=> ~ ( sK5 @ sK7 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1681]) ).
thf(f1681,plain,
( ( ( ( sK7 = sK7 )
=> ~ ( sK5 @ sK7 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1680]) ).
thf(f1680,plain,
( ( $true
= ( $true
=> ( ( sK7 = sK7 )
=> ~ ( sK5 @ sK7 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f1677,f1024]) ).
thf(f1024,plain,
( ( $true
= ( in @ sK7 @ sK2 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1014]) ).
thf(f1014,plain,
( ( $true
= ( $true
=> ( in @ sK7 @ sK2 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f56,f982]) ).
thf(f982,plain,
( ( $true
= ( in @ sK7 @ ( dsetconstr @ sK2 @ sK5 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f980]) ).
thf(f56,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f1677,plain,
( ! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( ( sK7 = X1 )
=> ~ ( sK5 @ X1 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1676]) ).
thf(f1676,plain,
( ! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( ( sK7 = X1 )
=> ( $false
= ( sK5 @ X1 ) ) ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1674,f1032]) ).
thf(f1032,plain,
( ( $false
= ( sK4 @ sK7 ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f1031]) ).
thf(f1031,plain,
( ( ( ~ ( sK4 @ sK7 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1030]) ).
thf(f1030,plain,
( ( ( $true
=> ~ ( sK4 @ sK7 ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f1010,f1024]) ).
thf(f1010,plain,
( ( ( ( in @ sK7 @ sK2 )
=> ~ ( sK4 @ sK7 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f998]) ).
thf(f998,plain,
( ( $true
= ( ( in @ sK7 @ sK2 )
=> ( ( sK4 @ sK7 )
=> $false ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f39,f989]) ).
thf(f989,plain,
( ( $false
= ( in @ sK7 @ ( dsetconstr @ sK2 @ sK4 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f988]) ).
thf(f988,plain,
( ( $false
= ( $true
=> ( in @ sK7 @ ( dsetconstr @ sK2 @ sK4 ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f980,f982]) ).
thf(f39,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f1674,plain,
( ! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ( sK7 = X1 )
=> ( ( sK4 @ sK7 )
= ( sK5 @ X1 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f1672]) ).
thf(f1672,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK7 = Y0 )
=> ( ( sK4 @ sK7 )
= ( sK5 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f1053]) ).
thf(f1053,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK7 = Y0 )
=> ( ( sK4 @ sK7 )
= ( sK5 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1045]) ).
thf(f1045,plain,
( ( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK7 = Y0 )
=> ( ( sK4 @ sK7 )
= ( sK5 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f148,f1024]) ).
thf(f148,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( X1 = Y0 )
=> ( ( sK4 @ X1 )
= ( sK5 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f147]) ).
thf(f147,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( Y0 = Y1 )
=> ( ( sK4 @ Y0 )
= ( sK5 @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( Y0 = Y1 )
=> ( ( sK4 @ Y0 )
= ( sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( Y0 = Y1 )
=> ( ( sK4 @ Y0 )
= ( sK5 @ Y1 ) ) ) ) ) ) )
=> ( ( dsetconstr @ sK2 @ sK4 )
= ( dsetconstr @ sK2 @ sK5 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f106,f92]) ).
thf(f92,plain,
sK2 = sK3,
inference(equality_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( sK3 = sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
= ( ( sK3 = sK2 )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK3 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ sK2 )
=> ( ( Y2 = Y3 )
=> ( ( Y0 @ Y2 )
= ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( dsetconstr @ sK3 @ Y0 )
= ( dsetconstr @ sK2 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
( $false
= ( ^ [Y0: $i] :
( ( Y0 = sK2 )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ sK2 )
=> ( ( Y3 = Y4 )
=> ( ( Y1 @ Y3 )
= ( Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y0 @ Y1 )
= ( dsetconstr @ sK2 @ Y2 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = sK2 )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ sK2 )
=> ( ( Y3 = Y4 )
=> ( ( Y1 @ Y3 )
= ( Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y0 @ Y1 )
= ( dsetconstr @ sK2 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1 @ Y2 )
= ( dsetconstr @ Y0 @ Y3 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1 @ Y2 )
= ( dsetconstr @ Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( Y4 = Y5 )
=> ( ( Y2 @ Y4 )
= ( Y3 @ Y5 ) ) ) ) ) ) )
=> ( ( dsetconstr @ Y1 @ Y2 )
= ( dsetconstr @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f106,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( Y0 = Y1 )
=> ( ( sK4 @ Y0 )
= ( sK5 @ Y1 ) ) ) ) ) ) )
=> ( ( dsetconstr @ sK3 @ sK4 )
= ( dsetconstr @ sK2 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( Y1 = Y2 )
=> ( ( sK4 @ Y1 )
= ( Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( dsetconstr @ sK3 @ sK4 )
= ( dsetconstr @ sK2 @ Y0 ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( Y1 = Y2 )
=> ( ( sK4 @ Y1 )
= ( Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( dsetconstr @ sK3 @ sK4 )
= ( dsetconstr @ sK2 @ Y0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK3 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ sK2 )
=> ( ( Y2 = Y3 )
=> ( ( Y0 @ Y2 )
= ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( dsetconstr @ sK3 @ Y0 )
= ( dsetconstr @ sK2 @ Y1 ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK3 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ sK2 )
=> ( ( Y2 = Y3 )
=> ( ( Y0 @ Y2 )
= ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( dsetconstr @ sK3 @ Y0 )
= ( dsetconstr @ sK2 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f90]) ).
thf(f90,plain,
( $false
= ( $true
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK3 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ sK2 )
=> ( ( Y2 = Y3 )
=> ( ( Y0 @ Y2 )
= ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( dsetconstr @ sK3 @ Y0 )
= ( dsetconstr @ sK2 @ Y1 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f86,f89]) ).
thf(f968,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f967]) ).
thf(f967,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f966]) ).
thf(f966,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f965]) ).
thf(f965,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f958,f214]) ).
thf(f214,plain,
( ( $true
= ( in @ sK6 @ sK2 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f207]) ).
thf(f207,plain,
( ( $true
= ( $true
=> ( in @ sK6 @ sK2 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f56,f188]) ).
thf(f188,plain,
( ( $true
= ( in @ sK6 @ ( dsetconstr @ sK2 @ sK4 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
( ( $false
= ( ( in @ sK6 @ ( dsetconstr @ sK2 @ sK4 ) )
=> ( in @ sK6 @ ( dsetconstr @ sK2 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f180]) ).
thf(f180,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) ) )
@ sK6 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f175]) ).
thf(f175,definition,
( spl0_2
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f958,plain,
( ( ( ~ ( in @ sK6 @ sK2 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f957]) ).
thf(f957,plain,
( ( ( ( in @ sK6 @ sK2 )
=> $false )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f956]) ).
thf(f956,plain,
( ( $true
= ( ( in @ sK6 @ sK2 )
=> ~ $true ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f955]) ).
thf(f955,plain,
( ( ( ( in @ sK6 @ sK2 )
=> ( sK6 != sK6 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f953]) ).
thf(f953,plain,
( ( ( ( in @ sK6 @ sK2 )
=> ( ( sK6 = sK6 )
=> $false ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f951,f227]) ).
thf(f227,plain,
( ( $false
= ( sK5 @ sK6 ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $true
= ( ~ ( sK5 @ sK6 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f221]) ).
thf(f221,plain,
( ( $true
= ( $true
=> ~ ( sK5 @ sK6 ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f203,f214]) ).
thf(f203,plain,
( ( ( ( in @ sK6 @ sK2 )
=> ~ ( sK5 @ sK6 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f193]) ).
thf(f193,plain,
( ( $true
= ( ( in @ sK6 @ sK2 )
=> ( ( sK5 @ sK6 )
=> $false ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f39,f190]) ).
thf(f190,plain,
( ( $false
= ( in @ sK6 @ ( dsetconstr @ sK2 @ sK5 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f189]) ).
thf(f189,plain,
( ( $false
= ( $true
=> ( in @ sK6 @ ( dsetconstr @ sK2 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f186,f188]) ).
thf(f951,plain,
( ! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ( sK6 = X1 )
=> ( sK5 @ X1 ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f950]) ).
thf(f950,plain,
( ! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( ( sK6 = X1 )
=> ( $true
= ( sK5 @ X1 ) ) ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f948,f220]) ).
thf(f220,plain,
( ( $true
= ( sK4 @ sK6 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f206]) ).
thf(f206,plain,
( ( $true
= ( $true
=> ( sK4 @ sK6 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f63,f188]) ).
thf(f948,plain,
( ! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( ( sK6 = X1 )
=> ( ( sK4 @ sK6 )
= ( sK5 @ X1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f946]) ).
thf(f946,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK6 = Y0 )
=> ( ( sK4 @ sK6 )
= ( sK5 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f243]) ).
thf(f243,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK6 = Y0 )
=> ( ( sK4 @ sK6 )
= ( sK5 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f238]) ).
thf(f238,plain,
( ( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK6 = Y0 )
=> ( ( sK4 @ sK6 )
= ( sK5 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f148,f214]) ).
thf(f177,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f170,f175,f172]) ).
thf(f170,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f114]) ).
thf(f114,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK5 ) )
=> ( in @ Y0 @ ( dsetconstr @ sK2 @ sK4 ) ) ) )
=> $false ) ) ),
inference(superposition,[status(thm)],[f74,f112]) ).
thf(f112,plain,
( $false
= ( ( dsetconstr @ sK2 @ sK4 )
= ( dsetconstr @ sK2 @ sK5 ) ) ),
inference(boolean_simplification,[status(thm)],[f111]) ).
thf(f111,plain,
( $false
= ( $true
=> ( ( dsetconstr @ sK2 @ sK4 )
= ( dsetconstr @ sK2 @ sK5 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f107,f110]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU558^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n006.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 12:26:45 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU558^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : A simple congruence property of dsetconstr
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (forall A:i.forall B:i.A = B -> (forall phi:i>o.forall psi:i>o.(
% 0.18/0.45 % forall x:i.in x A -> (forall y:i.in y B -> x = y -> (phi x <->
% 0.18/0.45 % psi y))) -> dsetconstr A (lambda x:i.phi x) = dsetconstr B
% 0.18/0.45 % (lambda x:i.psi x)))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC060l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v5.2.0, 0.60 v5.0.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 11 ( 4 unt; 6 typ; 4 def)
% 0.18/0.45 % Number of atoms : 27 ( 8 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 9 ( 5 avg)
% 0.18/0.45 % Number of connectives : 59 ( 0 ~; 0 |; 0 &; 41 @)
% 0.18/0.45 % ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 18 ( 4 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 24 ( 5 ^; 19 !; 0 ?; 24 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=45
% 0.18/0.45 % Bugfixes : v4.0.0 - Adding missing type delaration for in
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstr_type,type,
% 0.18/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrI_type,type,
% 0.18/0.45 dsetconstrI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrI,definition,
% 0.18/0.45 ( dsetconstrI
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( ( Xphi @ Xx )
% 0.18/0.45 => ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrEL_type,type,
% 0.18/0.45 dsetconstrEL: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrEL,definition,
% 0.18/0.45 ( dsetconstrEL
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrER_type,type,
% 0.18/0.45 dsetconstrER: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrER,definition,
% 0.18/0.45 ( dsetconstrER
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setext_type,type,
% 0.18/0.45 setext: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setext,definition,
% 0.18/0.45 ( setext
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xx @ B ) )
% 0.18/0.45 => ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) )
% 0.18/0.45 => ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstr__Cong,conjecture,
% 0.18/0.45 ( dsetconstrI
% 0.18/0.45 => ( dsetconstrEL
% 0.18/0.45 => ( dsetconstrER
% 0.18/0.45 => ( setext
% 0.18/0.45 => ! [A: $i,B: $i] :
% 0.18/0.45 ( ( A = B )
% 0.18/0.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ B )
% 0.18/0.45 => ( ( Xx = Xy )
% 0.18/0.45 => ( ( Xphi @ Xx )
% 0.18/0.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.18/0.45 => ( ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 = ( dsetconstr @ B
% 0.18/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.53/1.25 ---- Embedded in THF ---
% 1.53/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.25 %%% Generated on Tue Feb 24 12:26:46 EST 2026
% 1.53/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.25 %%% Logic specification used:
% 1.53/1.25 %%% thf(spec, logic, $$dhol).
% 1.53/1.25
% 1.53/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2DTF24719.p
% See solution above
% 1.53/1.25 ------------------------
% 1.53/1.26 ---- Cleaned THF ---
% 1.53/1.26 thf(in_type,type,
% 1.53/1.26 in: $i > $i > $o ).
% 1.53/1.26
% 1.53/1.26 thf(dsetconstr_type,type,
% 1.53/1.26 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.53/1.26
% 1.53/1.26 thf(dsetconstrI_type,type,
% 1.53/1.26 dsetconstrI: $o ).
% 1.53/1.26
% 1.53/1.26 thf(dsetconstrI,definition,
% 1.53/1.26 ( dsetconstrI
% 1.53/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.53/1.26 ( ( in @ Xx @ A )
% 1.53/1.26 => ( ( Xphi @ Xx )
% 1.53/1.26 => ( in @ Xx
% 1.53/1.26 @ ( dsetconstr @ A
% 1.53/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.53/1.26
% 1.53/1.26 thf(dsetconstrEL_type,type,
% 1.53/1.26 dsetconstrEL: $o ).
% 1.53/1.26
% 1.53/1.26 thf(dsetconstrEL,definition,
% 1.53/1.26 ( dsetconstrEL
% 1.53/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.53/1.26 ( ( in @ Xx
% 1.53/1.26 @ ( dsetconstr @ A
% 1.53/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.53/1.26 => ( in @ Xx @ A ) ) ) ) ).
% 1.53/1.26
% 1.53/1.26 thf(dsetconstrER_type,type,
% 1.53/1.26 dsetconstrER: $o ).
% 1.53/1.26
% 1.53/1.26 thf(dsetconstrER,definition,
% 1.53/1.26 ( dsetconstrER
% 1.53/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.53/1.26 ( ( in @ Xx
% 1.53/1.26 @ ( dsetconstr @ A
% 1.53/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.53/1.26 => ( Xphi @ Xx ) ) ) ) ).
% 1.53/1.26
% 1.53/1.26 thf(setext_type,type,
% 1.53/1.26 setext: $o ).
% 1.53/1.26
% 1.53/1.26 thf(setext,definition,
% 1.53/1.26 ( setext
% 1.53/1.26 = ( ! [A: $i,B: $i] :
% 1.53/1.26 ( ! [Xx: $i] :
% 1.53/1.26 ( ( in @ Xx @ A )
% 1.53/1.26 => ( in @ Xx @ B ) )
% 1.53/1.26 => ( ! [Xx: $i] :
% 1.53/1.26 ( ( in @ Xx @ B )
% 1.53/1.26 => ( in @ Xx @ A ) )
% 1.53/1.26 => ( A = B ) ) ) ) ) ).
% 1.53/1.26
% 1.53/1.26 thf(dsetconstr__Cong,conjecture,
% 1.53/1.26 ( dsetconstrI
% 1.53/1.26 => ( dsetconstrEL
% 1.53/1.26 => ( dsetconstrER
% 1.53/1.26 => ( setext
% 1.53/1.26 => ! [A: $i,B: $i] :
% 1.53/1.26 ( ( A = B )
% 1.53/1.26 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 1.53/1.26 ( ! [Xx: $i] :
% 1.53/1.26 ( ( in @ Xx @ A )
% 1.53/1.26 => ! [Xy: $i] :
% 1.53/1.26 ( ( in @ Xy @ B )
% 1.53/1.26 => ( ( Xx = Xy )
% 1.53/1.26 => ( ( Xphi @ Xx )
% 1.53/1.26 <=> ( Xpsi @ Xy ) ) ) ) )
% 1.53/1.26 => ( ( dsetconstr @ A
% 1.53/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.53/1.26 = ( dsetconstr @ B
% 1.53/1.26 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ) ).
% 1.53/1.26 ------------------------
% 1.53/1.27 % (24993)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_24719 for (3000ds/2Mi)
% 1.53/1.27 % (24993)Instruction limit reached!
% 1.53/1.27 % (24993)------------------------------
% 1.53/1.27 % (24993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (24993)Termination reason: Unknown
% 1.53/1.27 % (24993)Termination phase: Property scanning
% 1.53/1.27
% 1.53/1.27 % (24993)Memory used [KB]: 1023
% 1.53/1.27 % (24993)Time elapsed: 0.002 s
% 1.53/1.27 % (24993)Instructions burned: 3 (million)
% 1.53/1.27 % (24993)------------------------------
% 1.53/1.27 % (24993)------------------------------
% 1.53/1.28 % (24990)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_24719 for (3000ds/4Mi)
% 1.53/1.28 % (24989)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24719 for (3000ds/183Mi)
% 1.53/1.28 % (24991)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_24719 for (3000ds/27Mi)
% 1.53/1.28 % (24992)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24719 for (3000ds/2Mi)
% 1.53/1.28 % (24995)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24719 for (3000ds/18Mi)
% 1.53/1.28 % (24994)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_24719 for (3000ds/275Mi)
% 1.53/1.28 % (24992)Instruction limit reached!
% 1.53/1.28 % (24992)------------------------------
% 1.53/1.28 % (24992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (24992)Termination reason: Unknown
% 1.53/1.28 % (24992)Termination phase: Property scanning
% 1.53/1.28
% 1.53/1.28 % (24992)Memory used [KB]: 1023
% 1.53/1.28 % (24992)Time elapsed: 0.003 s
% 1.53/1.28 % (24992)Instructions burned: 2 (million)
% 1.53/1.28 % (24992)------------------------------
% 1.53/1.28 % (24992)------------------------------
% 1.53/1.28 % (24990)Instruction limit reached!
% 1.53/1.28 % (24990)------------------------------
% 1.53/1.28 % (24990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (24990)Termination reason: Unknown
% 1.53/1.28 % (24990)Termination phase: Property scanning
% 1.53/1.28
% 1.53/1.28 % (24990)Memory used [KB]: 1023
% 1.53/1.28 % (24990)Time elapsed: 0.004 s
% 1.53/1.28 % (24990)Instructions burned: 4 (million)
% 1.53/1.28 % (24990)------------------------------
% 1.53/1.28 % (24990)------------------------------
% 1.53/1.28 % (24996)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/3Mi)
% 1.53/1.29 % (24996)Instruction limit reached!
% 1.53/1.29 % (24996)------------------------------
% 1.53/1.29 % (24996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (24996)Termination reason: Unknown
% 1.53/1.29 % (24996)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (24996)Memory used [KB]: 5500
% 1.53/1.29 % (24996)Time elapsed: 0.003 s
% 1.53/1.29 % (24996)Instructions burned: 4 (million)
% 1.53/1.29 % (24996)------------------------------
% 1.53/1.29 % (24996)------------------------------
% 1.53/1.29 % (24995)Instruction limit reached!
% 1.53/1.29 % (24995)------------------------------
% 1.53/1.29 % (24995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (24995)Termination reason: Unknown
% 1.53/1.29 % (24995)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (24995)Memory used [KB]: 5628
% 1.53/1.29 % (24995)Time elapsed: 0.014 s
% 1.53/1.29 % (24995)Instructions burned: 19 (million)
% 1.53/1.29 % (24995)------------------------------
% 1.53/1.29 % (24995)------------------------------
% 1.53/1.30 % (24999)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_24719 for (2999ds/3Mi)
% 1.63/1.30 % (24999)Instruction limit reached!
% 1.63/1.30 % (24999)------------------------------
% 1.63/1.30 % (24999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (24999)Termination reason: Unknown
% 1.63/1.30 % (24999)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (24999)Memory used [KB]: 5500
% 1.63/1.30 % (24999)Time elapsed: 0.003 s
% 1.63/1.30 % (24999)Instructions burned: 4 (million)
% 1.63/1.30 % (24999)------------------------------
% 1.63/1.30 % (24999)------------------------------
% 1.63/1.30 % (24991)Instruction limit reached!
% 1.63/1.30 % (24991)------------------------------
% 1.63/1.30 % (24991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (24991)Termination reason: Unknown
% 1.63/1.30 % (24991)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (24991)Memory used [KB]: 5628
% 1.63/1.30 % (24991)Time elapsed: 0.019 s
% 1.63/1.30 % (24991)Instructions burned: 28 (million)
% 1.63/1.30 % (24991)------------------------------
% 1.63/1.30 % (24991)------------------------------
% 1.63/1.30 % (24997)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_24719 for (2999ds/37Mi)
% 1.63/1.30 % (24998)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_24719 for (2999ds/15Mi)
% 1.63/1.31 % (25001)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/7Mi)
% 1.63/1.31 % (24998)Instruction limit reached!
% 1.63/1.31 % (24998)------------------------------
% 1.63/1.31 % (24998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (24998)Termination reason: Unknown
% 1.63/1.31 % (24998)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (24998)Memory used [KB]: 5628
% 1.63/1.31 % (24998)Time elapsed: 0.011 s
% 1.63/1.31 % (24998)Instructions burned: 15 (million)
% 1.63/1.31 % (24998)------------------------------
% 1.63/1.31 % (24998)------------------------------
% 1.63/1.31 % (25001)Instruction limit reached!
% 1.63/1.31 % (25001)------------------------------
% 1.63/1.31 % (25001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (25001)Termination reason: Unknown
% 1.63/1.31 % (25001)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (25001)Memory used [KB]: 1023
% 1.63/1.31 % (25001)Time elapsed: 0.004 s
% 1.63/1.31 % (25001)Instructions burned: 8 (million)
% 1.63/1.31 % (25001)------------------------------
% 1.63/1.31 % (25001)------------------------------
% 1.63/1.31 % (25000)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_24719 for (2999ds/1041Mi)
% 1.63/1.31 % (25002)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/16Mi)
% 1.63/1.32 % (25002)Instruction limit reached!
% 1.63/1.32 % (25002)------------------------------
% 1.63/1.32 % (25002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (25002)Termination reason: Unknown
% 1.63/1.32 % (25002)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (25002)Memory used [KB]: 5756
% 1.63/1.32 % (25002)Time elapsed: 0.008 s
% 1.63/1.32 % (25002)Instructions burned: 16 (million)
% 1.63/1.32 % (25002)------------------------------
% 1.63/1.32 % (25002)------------------------------
% 1.63/1.32 % (25004)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_24719 for (2999ds/3Mi)
% 1.63/1.32 % (25004)Instruction limit reached!
% 1.63/1.32 % (25004)------------------------------
% 1.63/1.32 % (25004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (25004)Termination reason: Unknown
% 1.63/1.32 % (25004)Termination phase: Property scanning
% 1.63/1.32
% 1.63/1.32 % (25004)Memory used [KB]: 1023
% 1.63/1.32 % (25004)Time elapsed: 0.002 s
% 1.63/1.32 % (25004)Instructions burned: 4 (million)
% 1.63/1.32 % (25004)------------------------------
% 1.63/1.32 % (25004)------------------------------
% 1.63/1.32 % (24997)Instruction limit reached!
% 1.63/1.32 % (24997)------------------------------
% 1.63/1.32 % (24997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (24997)Termination reason: Unknown
% 1.63/1.32 % (24997)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (24997)Memory used [KB]: 5756
% 1.63/1.32 % (24997)Time elapsed: 0.025 s
% 1.63/1.32 % (24997)Instructions burned: 37 (million)
% 1.63/1.32 % (24997)------------------------------
% 1.63/1.32 % (24997)------------------------------
% 1.63/1.32 % (25003)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_24719 for (2999ds/3Mi)
% 1.63/1.32 % (25003)Instruction limit reached!
% 1.63/1.32 % (25003)------------------------------
% 1.63/1.32 % (25003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (25003)Termination reason: Unknown
% 1.63/1.32 % (25003)Termination phase: Preprocessing 3
% 1.63/1.32
% 1.63/1.32 % (25003)Memory used [KB]: 1023
% 1.63/1.32 % (25003)Time elapsed: 0.002 s
% 1.63/1.32 % (25003)Instructions burned: 3 (million)
% 1.63/1.32 % (25003)------------------------------
% 1.63/1.32 % (25003)------------------------------
% 1.63/1.33 % (25005)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/7Mi)
% 1.63/1.33 % (25005)Refutation not found, incomplete strategy
% 1.63/1.33 % (25005)------------------------------
% 1.63/1.33 % (25005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (25005)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.33
% 1.63/1.33
% 1.63/1.33 % (25005)Memory used [KB]: 5500
% 1.63/1.33 % (25005)Time elapsed: 0.003 s
% 1.63/1.33 % (25005)Instructions burned: 4 (million)
% 1.63/1.33 % (25005)------------------------------
% 1.63/1.33 % (25005)------------------------------
% 1.63/1.33 % (25006)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/3Mi)
% 1.63/1.33 % (25006)Instruction limit reached!
% 1.63/1.33 % (25006)------------------------------
% 1.63/1.33 % (25006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (25006)Termination reason: Unknown
% 1.63/1.33 % (25006)Termination phase: Property scanning
% 1.63/1.33
% 1.63/1.33 % (25006)Memory used [KB]: 1023
% 1.63/1.33 % (25006)Time elapsed: 0.002 s
% 1.63/1.33 % (25006)Instructions burned: 4 (million)
% 1.63/1.33 % (25006)------------------------------
% 1.63/1.33 % (25006)------------------------------
% 1.63/1.33 % (25008)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/18Mi)
% 1.63/1.34 % (25010)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/6Mi)
% 1.63/1.34 % (25009)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/710Mi)
% 1.63/1.34 % (25007)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/4Mi)
% 1.63/1.34 % (25008)Instruction limit reached!
% 1.63/1.34 % (25008)------------------------------
% 1.63/1.34 % (25008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (25008)Termination reason: Unknown
% 1.63/1.34 % (25008)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (25008)Memory used [KB]: 5628
% 1.63/1.34 % (25008)Time elapsed: 0.008 s
% 1.63/1.34 % (25008)Instructions burned: 18 (million)
% 1.63/1.34 % (25008)------------------------------
% 1.63/1.34 % (25008)------------------------------
% 1.63/1.34 % (25010)Instruction limit reached!
% 1.63/1.34 % (25010)------------------------------
% 1.63/1.34 % (25010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (25010)Termination reason: Unknown
% 1.63/1.34 % (25010)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (25010)Memory used [KB]: 5500
% 1.63/1.34 % (25010)Time elapsed: 0.003 s
% 1.63/1.34 % (25010)Instructions burned: 7 (million)
% 1.63/1.34 % (25010)------------------------------
% 1.63/1.34 % (25010)------------------------------
% 1.63/1.34 % (25007)Instruction limit reached!
% 1.63/1.34 % (25007)------------------------------
% 1.63/1.34 % (25007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (25007)Termination reason: Unknown
% 1.63/1.34 % (25007)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (25007)Memory used [KB]: 1023
% 1.63/1.34 % (25007)Time elapsed: 0.004 s
% 1.63/1.34 % (25007)Instructions burned: 4 (million)
% 1.63/1.34 % (25007)------------------------------
% 1.63/1.34 % (25007)------------------------------
% 1.63/1.35 % (25011)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/902Mi)
% 1.63/1.35 % (25012)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/21Mi)
% 1.63/1.36 % (25012)Instruction limit reached!
% 1.63/1.36 % (25012)------------------------------
% 1.63/1.36 % (25012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (25012)Termination reason: Unknown
% 1.63/1.36 % (25012)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (25012)Memory used [KB]: 5628
% 1.63/1.36 % (25012)Time elapsed: 0.008 s
% 1.63/1.36 % (25012)Instructions burned: 21 (million)
% 1.63/1.36 % (25012)------------------------------
% 1.63/1.36 % (25012)------------------------------
% 1.63/1.36 % (25013)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/5Mi)
% 1.63/1.36 % (25013)Instruction limit reached!
% 1.63/1.36 % (25013)------------------------------
% 1.63/1.36 % (25013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (25013)Termination reason: Unknown
% 1.63/1.36 % (25013)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (25013)Memory used [KB]: 5500
% 1.63/1.36 % (25013)Time elapsed: 0.005 s
% 1.63/1.36 % (25013)Instructions burned: 6 (million)
% 1.63/1.36 % (25013)------------------------------
% 1.63/1.36 % (25013)------------------------------
% 1.63/1.37 % (25014)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/6Mi)
% 1.63/1.37 % (25014)Instruction limit reached!
% 1.63/1.37 % (25014)------------------------------
% 1.63/1.37 % (25014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (25014)Termination reason: Unknown
% 1.63/1.37 % (25014)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (25014)Memory used [KB]: 5500
% 1.63/1.37 % (25014)Time elapsed: 0.003 s
% 1.63/1.37 % (25014)Instructions burned: 7 (million)
% 1.63/1.37 % (25014)------------------------------
% 1.63/1.37 % (25014)------------------------------
% 1.63/1.38 % (25016)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/779Mi)
% 1.63/1.38 % (25015)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_24719 for (2999ds/377Mi)
% 1.63/1.38 % (24989)Instruction limit reached!
% 1.63/1.38 % (24989)------------------------------
% 1.63/1.38 % (24989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (24989)Termination reason: Unknown
% 1.63/1.38 % (24989)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (24989)Memory used [KB]: 6524
% 1.63/1.38 % (24989)Time elapsed: 0.107 s
% 1.63/1.38 % (24989)Instructions burned: 183 (million)
% 1.63/1.38 % (24989)------------------------------
% 1.63/1.38 % (24989)------------------------------
% 1.63/1.40 % (25017)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_24719 for (2998ds/19Mi)
% 1.63/1.41 % (25017)Instruction limit reached!
% 1.63/1.41 % (25017)------------------------------
% 1.63/1.41 % (25017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.41 % (25017)Termination reason: Unknown
% 1.63/1.41 % (25017)Termination phase: Saturation
% 1.63/1.41
% 1.63/1.41 % (25017)Memory used [KB]: 5628
% 1.63/1.41 % (25017)Time elapsed: 0.008 s
% 1.63/1.41 % (25017)Instructions burned: 20 (million)
% 1.63/1.41 % (25017)------------------------------
% 1.63/1.41 % (25017)------------------------------
% 1.63/1.42 % (25018)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_24719 for (2998ds/879Mi)
% 1.63/1.43 % (24994)Instruction limit reached!
% 1.63/1.43 % (24994)------------------------------
% 1.63/1.43 % (24994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.43 % (24994)Termination reason: Unknown
% 1.63/1.43 % (24994)Termination phase: Saturation
% 1.63/1.43
% 1.63/1.43 % (24994)Memory used [KB]: 6268
% 1.63/1.43 % (24994)Time elapsed: 0.148 s
% 1.63/1.43 % (24994)Instructions burned: 277 (million)
% 1.63/1.43 % (24994)------------------------------
% 1.63/1.43 % (24994)------------------------------
% 1.63/1.44 % (25019)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_24719 for (2998ds/17Mi)
% 1.63/1.44 % (25019)Instruction limit reached!
% 1.63/1.44 % (25019)------------------------------
% 1.63/1.44 % (25019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (25019)Termination reason: Unknown
% 1.63/1.44 % (25019)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (25019)Memory used [KB]: 5628
% 1.63/1.44 % (25019)Time elapsed: 0.008 s
% 1.63/1.44 % (25019)Instructions burned: 18 (million)
% 1.63/1.44 % (25019)------------------------------
% 1.63/1.44 % (25019)------------------------------
% 1.63/1.45 % (25020)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24719 for (2998ds/3Mi)
% 1.63/1.45 % (25020)Instruction limit reached!
% 1.63/1.45 % (25020)------------------------------
% 1.63/1.45 % (25020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (25020)Termination reason: Unknown
% 1.63/1.45 % (25020)Termination phase: Saturation
% 1.63/1.45
% 1.63/1.45 % (25020)Memory used [KB]: 1023
% 1.63/1.45 % (25020)Time elapsed: 0.003 s
% 1.63/1.45 % (25020)Instructions burned: 5 (million)
% 1.63/1.45 % (25020)------------------------------
% 1.63/1.45 % (25020)------------------------------
% 1.63/1.46 % (25021)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_24719 for (2998ds/30Mi)
% 1.63/1.47 % (25021)Refutation not found, incomplete strategy
% 1.63/1.47 % (25021)------------------------------
% 1.63/1.47 % (25021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (25021)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.47
% 1.63/1.47
% 1.63/1.47 % (25021)Memory used [KB]: 5500
% 1.63/1.47 % (25021)Time elapsed: 0.004 s
% 1.63/1.47 % (25021)Instructions burned: 6 (million)
% 1.63/1.47 % (25021)------------------------------
% 1.63/1.47 % (25021)------------------------------
% 1.63/1.47 % (25000)First to succeed.
% 1.63/1.48 % (25000)Refutation found. Thanks to Tanya!
% 1.63/1.48 % SZS status Theorem for DTF2THF_24719
% 1.63/1.48 % SZS output start Proof for DTF2THF_24719
% 1.63/1.48 thf(func_def_0, type, in: $i > $i > $o).
% 1.63/1.48 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.63/1.48 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)).
% 1.63/1.48 thf(func_def_24, type, sK4: $i > $o).
% 1.63/1.48 thf(func_def_25, type, sK5: $i > $o).
% 1.63/1.48 thf(f1697,plain,(
% 1.63/1.48 $false),
% 1.63/1.48 inference(avatar_sat_refutation,[status(thm)],[f177,f968,f1696])).
% 1.63/1.48 thf(f1696,plain,(
% 1.63/1.48 ~spl0_1),
% 1.63/1.48 inference(avatar_contradiction_clause,[status(thm)],[f1695])).
% 1.63/1.48 thf(f1695,plain,(
% 1.63/1.48 $false | ~spl0_1),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f1694])).
% 1.63/1.48 thf(f1694,plain,(
% 1.63/1.48 ($false = $true) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f1693])).
% 1.63/1.48 thf(f1693,plain,(
% 1.63/1.48 ((~ $true) = $true) | ~spl0_1),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f1683,f987])).
% 1.63/1.48 thf(f987,plain,(
% 1.63/1.48 ((sK5 @ sK7) = $true) | ~spl0_1),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f986])).
% 1.63/1.48 thf(f986,plain,(
% 1.63/1.48 ((sK5 @ sK7) = $true) | ($false = $true) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f984])).
% 1.63/1.48 thf(f984,plain,(
% 1.63/1.48 ($false = ($false => (in @ sK7 @ (dsetconstr @ sK2 @ sK4)))) | ((sK5 @ sK7) = $true) | ~spl0_1),
% 1.63/1.48 inference(superposition,[status(thm)],[f980,f64])).
% 1.63/1.48 thf(f64,plain,(
% 1.63/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($false = (in @ X2 @ (dsetconstr @ X3 @ X1))) | ((X1 @ X2) = $true)) )),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.63/1.48 thf(f63,plain,(
% 1.63/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X2 @ (dsetconstr @ X3 @ X1)) => (X1 @ X2)) = $true)) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.63/1.48 thf(f62,plain,(
% 1.63/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ X2 @ (dsetconstr @ Y0 @ X1)) => (X1 @ X2))) @ X3) = $true)) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f61])).
% 1.63/1.48 thf(f61,plain,(
% 1.63/1.48 ( ! [X2 : $i,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (dsetconstr @ Y0 @ X1)) => (X1 @ X2)))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.63/1.48 thf(f60,plain,(
% 1.63/1.48 ( ! [X2 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (dsetconstr @ Y1 @ X1)) => (X1 @ Y0))))) @ X2))) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f59])).
% 1.63/1.48 thf(f59,plain,(
% 1.63/1.48 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (dsetconstr @ Y1 @ X1)) => (X1 @ Y0)))))) = $true)) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.63/1.48 thf(f58,plain,(
% 1.63/1.48 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1))))))) @ X1) = $true)) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f48])).
% 1.63/1.48 thf(f48,plain,(
% 1.63/1.48 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) = $true)),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.63/1.48 thf(f44,plain,(
% 1.63/1.48 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))))))),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f43])).
% 1.63/1.48 thf(f43,plain,(
% 1.63/1.48 ($false = ($true => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3))))))))))))))))),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f28,f42])).
% 1.63/1.48 thf(f42,plain,(
% 1.63/1.48 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) = $true)),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.63/1.48 thf(f28,plain,(
% 1.63/1.48 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3))))))))))))))))),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.63/1.48 thf(f25,plain,(
% 1.63/1.48 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))))))))),
% 1.63/1.48 inference(not_proxy_clausification,[status(thm)],[f24])).
% 1.63/1.48 thf(f24,plain,(
% 1.63/1.48 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3))))))))))))))))) = $true)),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.63/1.48 thf(f23,plain,(
% 1.63/1.48 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4))))))))))))))))))))),
% 1.63/1.48 inference(definition_unfolding,[status(thm)],[f20,f18,f19,f21,f22])).
% 1.63/1.48 thf(f22,plain,(
% 1.63/1.48 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.48 thf(f11,plain,(
% 1.63/1.48 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f10])).
% 1.63/1.48 thf(f10,plain,(
% 1.63/1.48 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 1.63/1.48 inference(rectify,[status(thm)],[f4])).
% 1.63/1.48 thf(f4,axiom,(
% 1.63/1.48 (setext = ! [X0 : $i,X4 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X4)) => (! [X2 : $i] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (X0 = X4))))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',setext)).
% 1.63/1.48 thf(f21,plain,(
% 1.63/1.48 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y1)))))))))),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f15])).
% 1.63/1.48 thf(f15,plain,(
% 1.63/1.48 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y1)))))))))),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f14])).
% 1.63/1.48 thf(f14,plain,(
% 1.63/1.48 (dsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X1)))),
% 1.63/1.48 inference(rectify,[status(thm)],[f3])).
% 1.63/1.48 thf(f3,axiom,(
% 1.63/1.48 (dsetconstrER = ! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',dsetconstrER)).
% 1.63/1.48 thf(f19,plain,(
% 1.63/1.48 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))))),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.48 thf(f13,plain,(
% 1.63/1.48 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))))),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f12])).
% 1.63/1.48 thf(f12,plain,(
% 1.63/1.48 (dsetconstrEL = ! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X0 @ X2)))),
% 1.63/1.48 inference(rectify,[status(thm)],[f2])).
% 1.63/1.48 thf(f2,axiom,(
% 1.63/1.48 (dsetconstrEL = ! [X2 : $i,X1 : $i > $o,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',dsetconstrEL)).
% 1.63/1.48 thf(f18,plain,(
% 1.63/1.48 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f9])).
% 1.63/1.48 thf(f9,plain,(
% 1.63/1.48 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f8])).
% 1.63/1.48 thf(f8,plain,(
% 1.63/1.48 (dsetconstrI = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 1.63/1.48 inference(rectify,[status(thm)],[f1])).
% 1.63/1.48 thf(f1,axiom,(
% 1.63/1.48 (dsetconstrI = ! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',dsetconstrI)).
% 1.63/1.48 thf(f20,plain,(
% 1.63/1.48 ((~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4))))))))))))))))))) = $true)),
% 1.63/1.48 inference(cnf_transformation,[status(thm)],[f17])).
% 1.63/1.48 thf(f17,plain,(
% 1.63/1.48 ((~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4))))))))))))))))))) = $true)),
% 1.63/1.48 inference(fool_elimination,[status(thm)],[f16])).
% 1.63/1.48 thf(f16,plain,(
% 1.63/1.48 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i > $o,X3 : $i > $o] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((X4 = X5) => ((X3 @ X4) <=> (X2 @ X5))))) => ((dsetconstr @ X0 @ (^[X6 : $i] : (X3 @ X6))) = (dsetconstr @ X1 @ (^[X7 : $i] : (X2 @ X7))))))))))),
% 1.63/1.48 inference(rectify,[status(thm)],[f6])).
% 1.63/1.48 thf(f6,negated_conjecture,(
% 1.63/1.48 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => ! [X0 : $i,X4 : $i] : ((X0 = X4) => ! [X5 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => ((X2 = X3) => ((X1 @ X2) <=> (X5 @ X3))))) => ((dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) = (dsetconstr @ X4 @ (^[X2 : $i] : (X5 @ X2))))))))))),
% 1.63/1.48 inference(negated_conjecture,[status(cth)],[f5])).
% 1.63/1.48 thf(f5,conjecture,(
% 1.63/1.48 dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => ! [X0 : $i,X4 : $i] : ((X0 = X4) => ! [X5 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => ((X2 = X3) => ((X1 @ X2) <=> (X5 @ X3))))) => ((dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) = (dsetconstr @ X4 @ (^[X2 : $i] : (X5 @ X2)))))))))),
% 1.63/1.48 file('/export/starexec/sandbox/tmp/tmp.dOP4dYVxNx/DTF2THF_24719.p',dsetconstr__Cong)).
% 1.63/1.48 thf(f980,plain,(
% 1.63/1.48 ($false = ((in @ sK7 @ (dsetconstr @ sK2 @ sK5)) => (in @ sK7 @ (dsetconstr @ sK2 @ sK4)))) | ~spl0_1),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f974])).
% 1.63/1.48 thf(f974,plain,(
% 1.63/1.48 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK5)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK4)))) @ sK7)) | ~spl0_1),
% 1.63/1.48 inference(sigma_clausification,[status(thm)],[f971])).
% 1.63/1.48 thf(f971,plain,(
% 1.63/1.48 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK5)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK4)))))) | ~spl0_1),
% 1.63/1.48 inference(not_proxy_clausification,[status(thm)],[f173])).
% 1.63/1.48 thf(f173,plain,(
% 1.63/1.48 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK5)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK4)))))) = $true) | ~spl0_1),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f172])).
% 1.63/1.48 thf(f172,definition,(
% 1.63/1.48 spl0_1 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK5)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK4)))))) = $true)),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.63/1.48 thf(f1683,plain,(
% 1.63/1.48 ((~ (sK5 @ sK7)) = $true) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f1682])).
% 1.63/1.48 thf(f1682,plain,(
% 1.63/1.48 ($true = ($true => (~ (sK5 @ sK7)))) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f1681])).
% 1.63/1.48 thf(f1681,plain,(
% 1.63/1.48 (((sK7 = sK7) => (~ (sK5 @ sK7))) = $true) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f1680])).
% 1.63/1.48 thf(f1680,plain,(
% 1.63/1.48 ($true = ($true => ((sK7 = sK7) => (~ (sK5 @ sK7))))) | ~spl0_1),
% 1.63/1.48 inference(superposition,[status(thm)],[f1677,f1024])).
% 1.63/1.48 thf(f1024,plain,(
% 1.63/1.48 ($true = (in @ sK7 @ sK2)) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f1014])).
% 1.63/1.48 thf(f1014,plain,(
% 1.63/1.48 ($true = ($true => (in @ sK7 @ sK2))) | ~spl0_1),
% 1.63/1.48 inference(superposition,[status(thm)],[f56,f982])).
% 1.63/1.48 thf(f982,plain,(
% 1.63/1.48 ($true = (in @ sK7 @ (dsetconstr @ sK2 @ sK5))) | ~spl0_1),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f980])).
% 1.63/1.48 thf(f56,plain,(
% 1.63/1.48 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((in @ X3 @ (dsetconstr @ X1 @ X2)) => (in @ X3 @ X1)) = $true)) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.63/1.48 thf(f55,plain,(
% 1.63/1.48 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (in @ Y0 @ X1))) @ X3))) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f54])).
% 1.63/1.48 thf(f54,plain,(
% 1.63/1.48 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (in @ Y0 @ X1)))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.63/1.48 thf(f53,plain,(
% 1.63/1.48 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (in @ Y1 @ X1))))) @ X2))) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f46])).
% 1.63/1.48 thf(f46,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (in @ Y1 @ X1)))))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.63/1.48 thf(f45,plain,(
% 1.63/1.48 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))) @ X1) = $true)) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f42])).
% 1.63/1.48 thf(f1677,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => ((sK7 = X1) => (~ (sK5 @ X1)))))) ) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f1676])).
% 1.63/1.48 thf(f1676,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => ((sK7 = X1) => ($false = (sK5 @ X1)))))) ) | ~spl0_1),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f1674,f1032])).
% 1.63/1.48 thf(f1032,plain,(
% 1.63/1.48 ($false = (sK4 @ sK7)) | ~spl0_1),
% 1.63/1.48 inference(not_proxy_clausification,[status(thm)],[f1031])).
% 1.63/1.48 thf(f1031,plain,(
% 1.63/1.48 ((~ (sK4 @ sK7)) = $true) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f1030])).
% 1.63/1.48 thf(f1030,plain,(
% 1.63/1.48 (($true => (~ (sK4 @ sK7))) = $true) | ~spl0_1),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f1010,f1024])).
% 1.63/1.48 thf(f1010,plain,(
% 1.63/1.48 (((in @ sK7 @ sK2) => (~ (sK4 @ sK7))) = $true) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f998])).
% 1.63/1.48 thf(f998,plain,(
% 1.63/1.48 ($true = ((in @ sK7 @ sK2) => ((sK4 @ sK7) => $false))) | ~spl0_1),
% 1.63/1.48 inference(superposition,[status(thm)],[f39,f989])).
% 1.63/1.48 thf(f989,plain,(
% 1.63/1.48 ($false = (in @ sK7 @ (dsetconstr @ sK2 @ sK4))) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f988])).
% 1.63/1.48 thf(f988,plain,(
% 1.63/1.48 ($false = ($true => (in @ sK7 @ (dsetconstr @ sK2 @ sK4)))) | ~spl0_1),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f980,f982])).
% 1.63/1.48 thf(f39,plain,(
% 1.63/1.48 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X2 @ X1) => ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3)))) = $true)) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.63/1.48 thf(f38,plain,(
% 1.63/1.48 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0))))) @ X3))) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f37])).
% 1.63/1.48 thf(f37,plain,(
% 1.63/1.48 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0)))))) = $true)) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.63/1.48 thf(f36,plain,(
% 1.63/1.48 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1))))))) @ X2))) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f35])).
% 1.63/1.48 thf(f35,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1)))))))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.63/1.48 thf(f34,plain,(
% 1.63/1.48 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2))))))))) @ X1) = $true)) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f29])).
% 1.63/1.48 thf(f29,plain,(
% 1.63/1.48 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) = $true)),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.63/1.48 thf(f1674,plain,(
% 1.63/1.48 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((sK7 = X1) => ((sK4 @ sK7) = (sK5 @ X1)))) = $true)) ) | ~spl0_1),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f1672])).
% 1.63/1.48 thf(f1672,plain,(
% 1.63/1.48 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK7 = Y0) => ((sK4 @ sK7) = (sK5 @ Y0))))) @ X1) = $true)) ) | ~spl0_1),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f1053])).
% 1.63/1.48 thf(f1053,plain,(
% 1.63/1.48 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK7 = Y0) => ((sK4 @ sK7) = (sK5 @ Y0)))))) = $true) | ~spl0_1),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f1045])).
% 1.63/1.48 thf(f1045,plain,(
% 1.63/1.48 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK7 = Y0) => ((sK4 @ sK7) = (sK5 @ Y0)))))))) | ~spl0_1),
% 1.63/1.48 inference(superposition,[status(thm)],[f148,f1024])).
% 1.63/1.48 thf(f148,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((X1 = Y0) => ((sK4 @ X1) = (sK5 @ Y0))))))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f147])).
% 1.63/1.48 thf(f147,plain,(
% 1.63/1.48 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((Y0 = Y1) => ((sK4 @ Y0) = (sK5 @ Y1)))))))) @ X1) = $true)) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f110])).
% 1.63/1.48 thf(f110,plain,(
% 1.63/1.48 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((Y0 = Y1) => ((sK4 @ Y0) = (sK5 @ Y1))))))))))),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.63/1.48 thf(f107,plain,(
% 1.63/1.48 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((Y0 = Y1) => ((sK4 @ Y0) = (sK5 @ Y1))))))))) => ((dsetconstr @ sK2 @ sK4) = (dsetconstr @ sK2 @ sK5))))),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f106,f92])).
% 1.63/1.48 thf(f92,plain,(
% 1.63/1.48 (sK2 = sK3)),
% 1.63/1.48 inference(equality_proxy_clausification,[status(thm)],[f89])).
% 1.63/1.48 thf(f89,plain,(
% 1.63/1.48 ((sK3 = sK2) = $true)),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.63/1.48 thf(f86,plain,(
% 1.63/1.48 ($false = ((sK3 = sK2) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK2) => ((Y2 = Y3) => ((Y0 @ Y2) = (Y1 @ Y3))))))))) => ((dsetconstr @ sK3 @ Y0) = (dsetconstr @ sK2 @ Y1)))))))))),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.63/1.48 thf(f85,plain,(
% 1.63/1.48 ($false = ((^[Y0 : $i]: ((Y0 = sK2) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ sK2) => ((Y3 = Y4) => ((Y1 @ Y3) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y1) = (dsetconstr @ sK2 @ Y2))))))))) @ sK3))),
% 1.63/1.48 inference(sigma_clausification,[status(thm)],[f81])).
% 1.63/1.48 thf(f81,plain,(
% 1.63/1.48 ($false = (!! @ $i @ (^[Y0 : $i]: ((Y0 = sK2) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ sK2) => ((Y3 = Y4) => ((Y1 @ Y3) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y1) = (dsetconstr @ sK2 @ Y2)))))))))))),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.63/1.48 thf(f80,plain,(
% 1.63/1.48 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3))))))))))) @ sK2))),
% 1.63/1.48 inference(sigma_clausification,[status(thm)],[f65])).
% 1.63/1.48 thf(f65,plain,(
% 1.63/1.48 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))))),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.63/1.48 thf(f47,plain,(
% 1.63/1.48 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3))))))))))))))),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.63/1.48 thf(f106,plain,(
% 1.63/1.48 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((Y0 = Y1) => ((sK4 @ Y0) = (sK5 @ Y1))))))))) => ((dsetconstr @ sK3 @ sK4) = (dsetconstr @ sK2 @ sK5))))),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.63/1.48 thf(f105,plain,(
% 1.63/1.48 ($false = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((Y1 = Y2) => ((sK4 @ Y1) = (Y0 @ Y2))))))))) => ((dsetconstr @ sK3 @ sK4) = (dsetconstr @ sK2 @ Y0)))) @ sK5))),
% 1.63/1.48 inference(sigma_clausification,[status(thm)],[f104])).
% 1.63/1.48 thf(f104,plain,(
% 1.63/1.48 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((Y1 = Y2) => ((sK4 @ Y1) = (Y0 @ Y2))))))))) => ((dsetconstr @ sK3 @ sK4) = (dsetconstr @ sK2 @ Y0))))) = $false)),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f103])).
% 1.63/1.48 thf(f103,plain,(
% 1.63/1.48 ($false = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK2) => ((Y2 = Y3) => ((Y0 @ Y2) = (Y1 @ Y3))))))))) => ((dsetconstr @ sK3 @ Y0) = (dsetconstr @ sK2 @ Y1)))))) @ sK4))),
% 1.63/1.48 inference(sigma_clausification,[status(thm)],[f91])).
% 1.63/1.48 thf(f91,plain,(
% 1.63/1.48 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK2) => ((Y2 = Y3) => ((Y0 @ Y2) = (Y1 @ Y3))))))))) => ((dsetconstr @ sK3 @ Y0) = (dsetconstr @ sK2 @ Y1))))))))),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f90])).
% 1.63/1.48 thf(f90,plain,(
% 1.63/1.48 ($false = ($true => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK2) => ((Y2 = Y3) => ((Y0 @ Y2) = (Y1 @ Y3))))))))) => ((dsetconstr @ sK3 @ Y0) = (dsetconstr @ sK2 @ Y1)))))))))),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f86,f89])).
% 1.63/1.48 thf(f968,plain,(
% 1.63/1.48 ~spl0_2),
% 1.63/1.48 inference(avatar_contradiction_clause,[status(thm)],[f967])).
% 1.63/1.48 thf(f967,plain,(
% 1.63/1.48 $false | ~spl0_2),
% 1.63/1.48 inference(trivial_inequality_removal,[status(thm)],[f966])).
% 1.63/1.48 thf(f966,plain,(
% 1.63/1.48 ($false = $true) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f965])).
% 1.63/1.48 thf(f965,plain,(
% 1.63/1.48 ((~ $true) = $true) | ~spl0_2),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f958,f214])).
% 1.63/1.48 thf(f214,plain,(
% 1.63/1.48 ($true = (in @ sK6 @ sK2)) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f207])).
% 1.63/1.48 thf(f207,plain,(
% 1.63/1.48 ($true = ($true => (in @ sK6 @ sK2))) | ~spl0_2),
% 1.63/1.48 inference(superposition,[status(thm)],[f56,f188])).
% 1.63/1.48 thf(f188,plain,(
% 1.63/1.48 ($true = (in @ sK6 @ (dsetconstr @ sK2 @ sK4))) | ~spl0_2),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f186])).
% 1.63/1.48 thf(f186,plain,(
% 1.63/1.48 ($false = ((in @ sK6 @ (dsetconstr @ sK2 @ sK4)) => (in @ sK6 @ (dsetconstr @ sK2 @ sK5)))) | ~spl0_2),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f180])).
% 1.63/1.48 thf(f180,plain,(
% 1.63/1.48 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK4)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK5)))) @ sK6)) | ~spl0_2),
% 1.63/1.48 inference(sigma_clausification,[status(thm)],[f176])).
% 1.63/1.48 thf(f176,plain,(
% 1.63/1.48 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK4)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK5)))))) | ~spl0_2),
% 1.63/1.48 inference(avatar_component_clause,[status(thm)],[f175])).
% 1.63/1.48 thf(f175,definition,(
% 1.63/1.48 spl0_2 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK4)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK5))))))),
% 1.63/1.48 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.63/1.48 thf(f958,plain,(
% 1.63/1.48 ((~ (in @ sK6 @ sK2)) = $true) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f957])).
% 1.63/1.48 thf(f957,plain,(
% 1.63/1.48 (((in @ sK6 @ sK2) => $false) = $true) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f956])).
% 1.63/1.48 thf(f956,plain,(
% 1.63/1.48 ($true = ((in @ sK6 @ sK2) => (~ $true))) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f955])).
% 1.63/1.48 thf(f955,plain,(
% 1.63/1.48 (((in @ sK6 @ sK2) => (~ (sK6 = sK6))) = $true) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f953])).
% 1.63/1.48 thf(f953,plain,(
% 1.63/1.48 (((in @ sK6 @ sK2) => ((sK6 = sK6) => $false)) = $true) | ~spl0_2),
% 1.63/1.48 inference(superposition,[status(thm)],[f951,f227])).
% 1.63/1.48 thf(f227,plain,(
% 1.63/1.48 ($false = (sK5 @ sK6)) | ~spl0_2),
% 1.63/1.48 inference(not_proxy_clausification,[status(thm)],[f222])).
% 1.63/1.48 thf(f222,plain,(
% 1.63/1.48 ($true = (~ (sK5 @ sK6))) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f221])).
% 1.63/1.48 thf(f221,plain,(
% 1.63/1.48 ($true = ($true => (~ (sK5 @ sK6)))) | ~spl0_2),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f203,f214])).
% 1.63/1.48 thf(f203,plain,(
% 1.63/1.48 (((in @ sK6 @ sK2) => (~ (sK5 @ sK6))) = $true) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f193])).
% 1.63/1.48 thf(f193,plain,(
% 1.63/1.48 ($true = ((in @ sK6 @ sK2) => ((sK5 @ sK6) => $false))) | ~spl0_2),
% 1.63/1.48 inference(superposition,[status(thm)],[f39,f190])).
% 1.63/1.48 thf(f190,plain,(
% 1.63/1.48 ($false = (in @ sK6 @ (dsetconstr @ sK2 @ sK5))) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f189])).
% 1.63/1.48 thf(f189,plain,(
% 1.63/1.48 ($false = ($true => (in @ sK6 @ (dsetconstr @ sK2 @ sK5)))) | ~spl0_2),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f186,f188])).
% 1.63/1.48 thf(f951,plain,(
% 1.63/1.48 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((sK6 = X1) => (sK5 @ X1))) = $true)) ) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f950])).
% 1.63/1.48 thf(f950,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => ((sK6 = X1) => ($true = (sK5 @ X1)))))) ) | ~spl0_2),
% 1.63/1.48 inference(forward_demodulation,[status(thm)],[f948,f220])).
% 1.63/1.48 thf(f220,plain,(
% 1.63/1.48 ($true = (sK4 @ sK6)) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f206])).
% 1.63/1.48 thf(f206,plain,(
% 1.63/1.48 ($true = ($true => (sK4 @ sK6))) | ~spl0_2),
% 1.63/1.48 inference(superposition,[status(thm)],[f63,f188])).
% 1.63/1.48 thf(f948,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => ((sK6 = X1) => ((sK4 @ sK6) = (sK5 @ X1)))))) ) | ~spl0_2),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f946])).
% 1.63/1.48 thf(f946,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK6 = Y0) => ((sK4 @ sK6) = (sK5 @ Y0))))) @ X1))) ) | ~spl0_2),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f243])).
% 1.63/1.48 thf(f243,plain,(
% 1.63/1.48 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK6 = Y0) => ((sK4 @ sK6) = (sK5 @ Y0))))))) | ~spl0_2),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f238])).
% 1.63/1.48 thf(f238,plain,(
% 1.63/1.48 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK6 = Y0) => ((sK4 @ sK6) = (sK5 @ Y0)))))))) | ~spl0_2),
% 1.63/1.48 inference(superposition,[status(thm)],[f148,f214])).
% 1.63/1.48 thf(f177,plain,(
% 1.63/1.48 spl0_1 | spl0_2),
% 1.63/1.48 inference(avatar_split_clause,[status(thm)],[f170,f175,f172])).
% 1.63/1.48 thf(f170,plain,(
% 1.63/1.48 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK4)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK5)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK5)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK4)))))) = $true)),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.63/1.48 thf(f119,plain,(
% 1.63/1.48 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK4)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK5))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK5)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK4))))))) = $true)),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f114])).
% 1.63/1.48 thf(f114,plain,(
% 1.63/1.48 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK4)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK5))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK5)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK4))))) => $false)))),
% 1.63/1.48 inference(superposition,[status(thm)],[f74,f112])).
% 1.63/1.48 thf(f112,plain,(
% 1.63/1.48 ($false = ((dsetconstr @ sK2 @ sK4) = (dsetconstr @ sK2 @ sK5)))),
% 1.63/1.48 inference(boolean_simplification,[status(thm)],[f111])).
% 1.63/1.48 thf(f111,plain,(
% 1.63/1.48 ($false = ($true => ((dsetconstr @ sK2 @ sK4) = (dsetconstr @ sK2 @ sK5))))),
% 1.63/1.48 inference(backward_demodulation,[status(thm)],[f107,f110])).
% 1.63/1.48 thf(f74,plain,(
% 1.63/1.48 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.63/1.48 thf(f73,plain,(
% 1.63/1.48 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2) = $true)) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f72])).
% 1.63/1.48 thf(f72,plain,(
% 1.63/1.48 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1))))) = $true)) )),
% 1.63/1.48 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.63/1.48 thf(f71,plain,(
% 1.63/1.48 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1) = $true)) )),
% 1.63/1.48 inference(pi_clausification,[status(thm)],[f66])).
% 1.63/1.48 thf(f66,plain,(
% 1.63/1.48 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.63/1.48 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.63/1.48 % SZS output end Proof for DTF2THF_24719
% 1.63/1.48 % (25000)------------------------------
% 1.63/1.48 % (25000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.48 % (25000)Termination reason: Refutation
% 1.63/1.48
% 1.63/1.48 % (25000)Memory used [KB]: 6652
% 1.63/1.48 % (25000)Time elapsed: 0.167 s
% 1.63/1.48 % (25000)Instructions burned: 349 (million)
% 1.63/1.48 % (25000)------------------------------
% 1.63/1.48 % (25000)------------------------------
% 1.63/1.48 % (24988)Success in time 0.217 s
%------------------------------------------------------------------------------