%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV138^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 09:40:22 AM UTC 2026
% Result : Theorem 1.69s 1.36s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 4
% Syntax : Number of formulae : 64 ( 38 unt; 0 typ; 3 def)
% Number of atoms : 543 ( 56 equ; 0 cnn)
% Maximal formula atoms : 3 ( 8 avg)
% Number of connectives : 1675 ( 25 ~; 22 |; 150 &;1031 @)
% ( 3 <=>; 211 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 12 con; 0-2 aty)
% ( 233 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 305 ( 245 ^; 60 !; 0 ?; 305 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > a > $o ).
thf(func_def_19,type,
sK3: a ).
thf(func_def_20,type,
sK4: a ).
thf(func_def_21,type,
sK5: a ).
thf(func_def_22,type,
sK6: a > $o ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: a ).
thf(func_def_25,type,
sK9: a ).
thf(f182,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f82,f121,f162,f177]) ).
thf(f177,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f176]) ).
thf(f176,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f173]) ).
thf(f173,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f135,f169]) ).
thf(f169,plain,
( ( $false
= ( ( sK2 @ sK3 @ sK9 )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f165]) ).
thf(f165,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f161]) ).
thf(f161,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f160]) ).
thf(f160,definition,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f135,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ sK3 @ X0 )
=> ( sK6 @ X0 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f127]) ).
thf(f127,plain,
( ! [X0: a] :
( ( ( ( sK2 @ sK3 @ X0 )
& $true )
=> ( sK6 @ X0 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f65,f78]) ).
thf(f78,plain,
( ( ( sK6 @ sK3 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl0_1
<=> ( ( sK6 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f65,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X2 @ X1 )
& ( sK6 @ X2 ) )
=> ( sK6 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a,X3: a > a > $o] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X3 @ X2 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X7 )
& ( X3 @ X7 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X0 ) )
& ! [X8: a > $o] :
( ( ! [X9: a] :
( ( X3 @ X1 @ X9 )
=> ( X8 @ X9 ) )
& ! [X10: a,X11: a] :
( ( ( X8 @ X11 )
& ( X3 @ X11 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X2 ) ) )
=> ! [X12: a > $o] :
( ( ! [X13: a] :
( ( X3 @ X1 @ X13 )
=> ( X12 @ X13 ) )
& ! [X14: a,X15: a] :
( ( ( X12 @ X14 )
& ( X3 @ X14 @ X15 ) )
=> ( X12 @ X15 ) ) )
=> ( X12 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X1: a,X2: a,X0: a > a > $o] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X1 @ X5 )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X2 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X1 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: a,X1: a,X2: a,X0: a > a > $o] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X1 @ X5 )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X2 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X1 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oGq4bMr1yX/DTF2THF_24689.p',cTHM150_pme) ).
thf(f162,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f156,f160,f80]) ).
thf(f80,definition,
( spl0_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f156,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false ) ),
inference(superposition,[status(thm)],[f37,f26]) ).
thf(f26,plain,
( $false
= ( sK6 @ sK5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f37,plain,
! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f19,f33]) ).
thf(f33,plain,
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f121,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f120]) ).
thf(f120,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f113,f65]) ).
thf(f113,plain,
( ( ( ( ( sK2 @ sK7 @ sK8 )
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
& ( sK6 @ sK7 ) )
=> ( sK6 @ Y0 ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
& ( sK6 @ sK7 ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f82,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f75,f80,f77]) ).
thf(f75,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ( ( sK6 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
=> ( sK6 @ sK3 ) ) ),
inference(boolean_simplification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& $true )
=> ( sK6 @ sK3 ) )
= $true ),
inference(superposition,[status(thm)],[f54,f41]) ).
thf(f41,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f40]) ).
thf(f40,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f27,f39]) ).
thf(f54,plain,
! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV138^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:40:25 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEV138^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory (Relations)
% 0.30/0.46 % Problem : TPS problem THM150
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : The transitive closure TC2 of a relation is transitive.
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0495 [Bro09]
% 0.30/0.46 % : tps_1086 [Bro09]
% 0.30/0.46 % : THM150 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.30/0.46 % Number of connectives : 41 ( 0 ~; 0 |; 7 &; 24 @)
% 0.30/0.46 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 16 ( 16 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.30/0.46 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % : Polymorphic definitions expanded.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM150_pme,conjecture,
% 0.30/0.46 ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
% 0.30/0.46 ( ( ! [Xq: a > $o] :
% 0.30/0.46 ( ( ! [Xw: a] :
% 0.30/0.46 ( ( Xr @ Xx @ Xw )
% 0.30/0.46 => ( Xq @ Xw ) )
% 0.30/0.46 & ! [Xu: a,Xv: a] :
% 0.30/0.46 ( ( ( Xq @ Xu )
% 0.30/0.46 & ( Xr @ Xu @ Xv ) )
% 0.30/0.46 => ( Xq @ Xv ) ) )
% 0.30/0.46 => ( Xq @ Xy ) )
% 0.30/0.46 & ! [Xq: a > $o] :
% 0.30/0.46 ( ( ! [Xw: a] :
% 0.30/0.46 ( ( Xr @ Xy @ Xw )
% 0.30/0.46 => ( Xq @ Xw ) )
% 0.30/0.46 & ! [Xu: a,Xv: a] :
% 0.30/0.46 ( ( ( Xq @ Xu )
% 0.30/0.46 & ( Xr @ Xu @ Xv ) )
% 0.30/0.46 => ( Xq @ Xv ) ) )
% 0.30/0.46 => ( Xq @ Xz ) ) )
% 0.30/0.46 => ! [Xq: a > $o] :
% 0.30/0.46 ( ( ! [Xw: a] :
% 0.30/0.46 ( ( Xr @ Xx @ Xw )
% 0.30/0.46 => ( Xq @ Xw ) )
% 0.30/0.46 & ! [Xu: a,Xv: a] :
% 0.30/0.46 ( ( ( Xq @ Xu )
% 0.30/0.46 & ( Xr @ Xu @ Xv ) )
% 0.30/0.46 => ( Xq @ Xv ) ) )
% 0.30/0.46 => ( Xq @ Xz ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.49/1.29 ---- Embedded in THF ---
% 1.49/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.29 %%% Generated on Tue Feb 24 12:40:26 EST 2026
% 1.49/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.29 %%% Logic specification used:
% 1.49/1.29 %%% thf(spec, logic, $$dhol).
% 1.49/1.29
% 1.49/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oGq4bMr1yX/DTF2DTF24689.p
% See solution above
% 1.49/1.29 ------------------------
% 1.69/1.30 ---- Cleaned THF ---
% 1.69/1.30 thf(a_type,type,
% 1.69/1.30 a: $tType ).
% 1.69/1.30
% 1.69/1.30 thf(cTHM150_pme,conjecture,
% 1.69/1.30 ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
% 1.69/1.30 ( ( ! [Xq: a > $o] :
% 1.69/1.30 ( ( ! [Xw: a] :
% 1.69/1.30 ( ( Xr @ Xx @ Xw )
% 1.69/1.30 => ( Xq @ Xw ) )
% 1.69/1.30 & ! [Xu: a,Xv: a] :
% 1.69/1.30 ( ( ( Xq @ Xu )
% 1.69/1.30 & ( Xr @ Xu @ Xv ) )
% 1.69/1.30 => ( Xq @ Xv ) ) )
% 1.69/1.30 => ( Xq @ Xy ) )
% 1.69/1.30 & ! [Xq: a > $o] :
% 1.69/1.30 ( ( ! [Xw: a] :
% 1.69/1.30 ( ( Xr @ Xy @ Xw )
% 1.69/1.30 => ( Xq @ Xw ) )
% 1.69/1.30 & ! [Xu: a,Xv: a] :
% 1.69/1.30 ( ( ( Xq @ Xu )
% 1.69/1.30 & ( Xr @ Xu @ Xv ) )
% 1.69/1.30 => ( Xq @ Xv ) ) )
% 1.69/1.30 => ( Xq @ Xz ) ) )
% 1.69/1.30 => ! [Xq: a > $o] :
% 1.69/1.30 ( ( ! [Xw: a] :
% 1.69/1.30 ( ( Xr @ Xx @ Xw )
% 1.69/1.30 => ( Xq @ Xw ) )
% 1.69/1.30 & ! [Xu: a,Xv: a] :
% 1.69/1.30 ( ( ( Xq @ Xu )
% 1.69/1.30 & ( Xr @ Xu @ Xv ) )
% 1.69/1.30 => ( Xq @ Xv ) ) )
% 1.69/1.30 => ( Xq @ Xz ) ) ) ).
% 1.69/1.30 ------------------------
% 1.69/1.31 % (24787)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_24689 for (3000ds/4Mi)
% 1.69/1.31 % (24787)Instruction limit reached!
% 1.69/1.31 % (24787)------------------------------
% 1.69/1.31 % (24787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (24787)Termination reason: Unknown
% 1.69/1.31 % (24787)Termination phase: Saturation
% 1.69/1.31
% 1.69/1.31 % (24787)Memory used [KB]: 5500
% 1.69/1.31 % (24787)Time elapsed: 0.004 s
% 1.69/1.31 % (24787)Instructions burned: 6 (million)
% 1.69/1.31 % (24787)------------------------------
% 1.69/1.31 % (24787)------------------------------
% 1.69/1.32 % (24786)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24689 for (3000ds/183Mi)
% 1.69/1.32 % (24788)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_24689 for (3000ds/27Mi)
% 1.69/1.32 % (24789)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24689 for (3000ds/2Mi)
% 1.69/1.32 % (24790)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_24689 for (3000ds/2Mi)
% 1.69/1.32 % (24791)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_24689 for (3000ds/275Mi)
% 1.69/1.32 % (24792)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24689 for (3000ds/18Mi)
% 1.69/1.32 % (24789)Instruction limit reached!
% 1.69/1.32 % (24789)------------------------------
% 1.69/1.32 % (24789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (24789)Termination reason: Unknown
% 1.69/1.32 % (24789)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (24789)Memory used [KB]: 5500
% 1.69/1.32 % (24789)Time elapsed: 0.004 s
% 1.69/1.32 % (24789)Instructions burned: 3 (million)
% 1.69/1.32 % (24789)------------------------------
% 1.69/1.32 % (24789)------------------------------
% 1.69/1.32 % (24790)Instruction limit reached!
% 1.69/1.32 % (24790)------------------------------
% 1.69/1.32 % (24790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (24790)Termination reason: Unknown
% 1.69/1.32 % (24790)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (24790)Memory used [KB]: 5500
% 1.69/1.32 % (24790)Time elapsed: 0.004 s
% 1.69/1.32 % (24790)Instructions burned: 3 (million)
% 1.69/1.32 % (24790)------------------------------
% 1.69/1.32 % (24790)------------------------------
% 1.69/1.32 % (24793)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24689 for (2999ds/3Mi)
% 1.69/1.33 % (24793)Instruction limit reached!
% 1.69/1.33 % (24793)------------------------------
% 1.69/1.33 % (24793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (24793)Termination reason: Unknown
% 1.69/1.33 % (24793)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (24793)Memory used [KB]: 5500
% 1.69/1.33 % (24793)Time elapsed: 0.002 s
% 1.69/1.33 % (24793)Instructions burned: 3 (million)
% 1.69/1.33 % (24793)------------------------------
% 1.69/1.33 % (24793)------------------------------
% 1.69/1.33 % (24792)Instruction limit reached!
% 1.69/1.33 % (24792)------------------------------
% 1.69/1.33 % (24792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (24792)Termination reason: Unknown
% 1.69/1.33 % (24792)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (24792)Memory used [KB]: 5628
% 1.69/1.33 % (24792)Time elapsed: 0.013 s
% 1.69/1.33 % (24792)Instructions burned: 18 (million)
% 1.69/1.33 % (24792)------------------------------
% 1.69/1.33 % (24792)------------------------------
% 1.69/1.33 % (24796)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_24689 for (2999ds/3Mi)
% 1.69/1.34 % (24796)Instruction limit reached!
% 1.69/1.34 % (24796)------------------------------
% 1.69/1.34 % (24796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (24796)Termination reason: Unknown
% 1.69/1.34 % (24796)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (24796)Memory used [KB]: 5500
% 1.69/1.34 % (24796)Time elapsed: 0.002 s
% 1.69/1.34 % (24796)Instructions burned: 3 (million)
% 1.69/1.34 % (24796)------------------------------
% 1.69/1.34 % (24796)------------------------------
% 1.69/1.34 % (24788)Instruction limit reached!
% 1.69/1.34 % (24788)------------------------------
% 1.69/1.34 % (24788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (24788)Termination reason: Unknown
% 1.69/1.34 % (24788)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (24788)Memory used [KB]: 5628
% 1.69/1.34 % (24788)Time elapsed: 0.021 s
% 1.69/1.34 % (24788)Instructions burned: 27 (million)
% 1.69/1.34 % (24788)------------------------------
% 1.69/1.34 % (24788)------------------------------
% 1.69/1.34 % (24794)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_24689 for (2999ds/37Mi)
% 1.69/1.34 % (24795)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_24689 for (2999ds/15Mi)
% 1.69/1.34 % (24797)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_24689 for (2999ds/1041Mi)
% 1.69/1.34 % (24798)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24689 for (2999ds/7Mi)
% 1.69/1.35 % (24798)Instruction limit reached!
% 1.69/1.35 % (24798)------------------------------
% 1.69/1.35 % (24798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (24798)Termination reason: Unknown
% 1.69/1.35 % (24798)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (24798)Memory used [KB]: 1023
% 1.69/1.35 % (24798)Time elapsed: 0.004 s
% 1.69/1.35 % (24798)Instructions burned: 9 (million)
% 1.69/1.35 % (24798)------------------------------
% 1.69/1.35 % (24798)------------------------------
% 1.69/1.35 % (24795)Instruction limit reached!
% 1.69/1.35 % (24795)------------------------------
% 1.69/1.35 % (24795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (24795)Termination reason: Unknown
% 1.69/1.35 % (24795)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (24795)Memory used [KB]: 5628
% 1.69/1.35 % (24795)Time elapsed: 0.012 s
% 1.69/1.35 % (24795)Instructions burned: 15 (million)
% 1.69/1.35 % (24795)------------------------------
% 1.69/1.35 % (24795)------------------------------
% 1.69/1.36 % (24799)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24689 for (2999ds/16Mi)
% 1.69/1.36 % (24794)Instruction limit reached!
% 1.69/1.36 % (24794)------------------------------
% 1.69/1.36 % (24794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (24794)Termination reason: Unknown
% 1.69/1.36 % (24794)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (24794)Memory used [KB]: 5884
% 1.69/1.36 % (24794)Time elapsed: 0.019 s
% 1.69/1.36 % (24794)Instructions burned: 38 (million)
% 1.69/1.36 % (24794)------------------------------
% 1.69/1.36 % (24794)------------------------------
% 1.69/1.36 % (24800)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_24689 for (2999ds/3Mi)
% 1.69/1.36 % (24797)First to succeed.
% 1.69/1.36 % (24800)Instruction limit reached!
% 1.69/1.36 % (24800)------------------------------
% 1.69/1.36 % (24800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (24800)Termination reason: Unknown
% 1.69/1.36 % (24800)Termination phase: Property scanning
% 1.69/1.36
% 1.69/1.36 % (24800)Memory used [KB]: 1023
% 1.69/1.36 % (24800)Time elapsed: 0.002 s
% 1.69/1.36 % (24800)Instructions burned: 3 (million)
% 1.69/1.36 % (24800)------------------------------
% 1.69/1.36 % (24800)------------------------------
% 1.69/1.36 % (24797)Refutation found. Thanks to Tanya!
% 1.69/1.36 % SZS status Theorem for DTF2THF_24689
% 1.69/1.36 % SZS output start Proof for DTF2THF_24689
% 1.69/1.36 thf(type_def_5, type, a: $tType).
% 1.69/1.36 thf(func_def_0, type, a: $tType).
% 1.69/1.36 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.69/1.36 thf(func_def_18, type, sK2: a > a > $o).
% 1.69/1.36 thf(func_def_19, type, sK3: a).
% 1.69/1.36 thf(func_def_20, type, sK4: a).
% 1.69/1.36 thf(func_def_21, type, sK5: a).
% 1.69/1.36 thf(func_def_22, type, sK6: a > $o).
% 1.69/1.36 thf(func_def_23, type, sK7: a).
% 1.69/1.36 thf(func_def_24, type, sK8: a).
% 1.69/1.36 thf(func_def_25, type, sK9: a).
% 1.69/1.36 thf(f182,plain,(
% 1.69/1.36 $false),
% 1.69/1.36 inference(avatar_sat_refutation,[status(thm)],[f82,f121,f162,f177])).
% 1.69/1.36 thf(f177,plain,(
% 1.69/1.36 ~spl0_1 | ~spl0_3),
% 1.69/1.36 inference(avatar_contradiction_clause,[status(thm)],[f176])).
% 1.69/1.36 thf(f176,plain,(
% 1.69/1.36 $false | (~spl0_1 | ~spl0_3)),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f173])).
% 1.69/1.36 thf(f173,plain,(
% 1.69/1.36 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 1.69/1.36 inference(superposition,[status(thm)],[f135,f169])).
% 1.69/1.36 thf(f169,plain,(
% 1.69/1.36 ($false = ((sK2 @ sK3 @ sK9) => (sK6 @ sK9))) | ~spl0_3),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f165])).
% 1.69/1.36 thf(f165,plain,(
% 1.69/1.36 (((^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0))) @ sK9) = $false) | ~spl0_3),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f161])).
% 1.69/1.36 thf(f161,plain,(
% 1.69/1.36 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))) = $false) | ~spl0_3),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f160])).
% 1.69/1.36 thf(f160,definition,(
% 1.69/1.36 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))) = $false)),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.69/1.36 thf(f135,plain,(
% 1.69/1.36 ( ! [X0 : a] : (($true = ((sK2 @ sK3 @ X0) => (sK6 @ X0)))) ) | ~spl0_1),
% 1.69/1.36 inference(boolean_simplification,[status(thm)],[f127])).
% 1.69/1.36 thf(f127,plain,(
% 1.69/1.36 ( ! [X0 : a] : (((((sK2 @ sK3 @ X0) & $true) => (sK6 @ X0)) = $true)) ) | ~spl0_1),
% 1.69/1.36 inference(superposition,[status(thm)],[f65,f78])).
% 1.69/1.36 thf(f78,plain,(
% 1.69/1.36 ((sK6 @ sK3) = $true) | ~spl0_1),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.69/1.36 thf(f77,definition,(
% 1.69/1.36 spl0_1 <=> ((sK6 @ sK3) = $true)),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.69/1.36 thf(f65,plain,(
% 1.69/1.36 ( ! [X2 : a,X1 : a] : (($true = (((sK2 @ X2 @ X1) & (sK6 @ X2)) => (sK6 @ X1)))) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.69/1.36 thf(f64,plain,(
% 1.69/1.36 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ Y0 @ X1) & (sK6 @ Y0)) => (sK6 @ X1))) @ X2) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f63])).
% 1.69/1.36 thf(f63,plain,(
% 1.69/1.36 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) & (sK6 @ Y0)) => (sK6 @ X1)))))) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.69/1.36 thf(f62,plain,(
% 1.69/1.36 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0))))) @ X1))) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f39])).
% 1.69/1.36 thf(f39,plain,(
% 1.69/1.36 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))))),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.69/1.36 thf(f27,plain,(
% 1.69/1.36 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))))))),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.69/1.36 thf(f25,plain,(
% 1.69/1.36 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))))) => (sK6 @ sK5)))),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.69/1.36 thf(f24,plain,(
% 1.69/1.36 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK5))) @ sK6) = $false)),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f18])).
% 1.69/1.36 thf(f18,plain,(
% 1.69/1.36 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK5)))))),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.69/1.36 thf(f17,plain,(
% 1.69/1.36 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK3)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK5))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK5))))))),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.69/1.36 thf(f16,plain,(
% 1.69/1.36 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK3)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) @ sK5))),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f15])).
% 1.69/1.36 thf(f15,plain,(
% 1.69/1.36 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK3)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))))))),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.69/1.36 thf(f14,plain,(
% 1.69/1.36 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ sK3)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))))))) @ sK4))),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f13])).
% 1.69/1.36 thf(f13,plain,(
% 1.69/1.36 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ sK3)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))))))))),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.69/1.36 thf(f12,plain,(
% 1.69/1.36 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))) @ sK3) = $false)),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f11])).
% 1.69/1.36 thf(f11,plain,(
% 1.69/1.36 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))))))))) = $false)),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.69/1.36 thf(f10,plain,(
% 1.69/1.36 (((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y1)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))))))))))) @ sK2) = $false)),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f7])).
% 1.69/1.36 thf(f7,plain,(
% 1.69/1.36 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y1)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))))))))))) = $false)),
% 1.69/1.36 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.69/1.36 thf(f6,plain,(
% 1.69/1.36 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y1)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))))))))))))))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f5])).
% 1.69/1.36 thf(f5,plain,(
% 1.69/1.36 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y1)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))))))))))))))),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.69/1.36 thf(f4,plain,(
% 1.69/1.36 ~! [X0 : a,X1 : a,X2 : a,X3 : a > a > $o] : ((! [X4 : a > $o] : ((! [X5 : a] : ((X3 @ X2 @ X5) => (X4 @ X5)) & ! [X6 : a,X7 : a] : (((X4 @ X7) & (X3 @ X7 @ X6)) => (X4 @ X6))) => (X4 @ X0)) & ! [X8 : a > $o] : ((! [X9 : a] : ((X3 @ X1 @ X9) => (X8 @ X9)) & ! [X10 : a,X11 : a] : (((X8 @ X11) & (X3 @ X11 @ X10)) => (X8 @ X10))) => (X8 @ X2))) => ! [X12 : a > $o] : ((! [X13 : a] : ((X3 @ X1 @ X13) => (X12 @ X13)) & ! [X14 : a,X15 : a] : (((X12 @ X14) & (X3 @ X14 @ X15)) => (X12 @ X15))) => (X12 @ X0)))),
% 1.69/1.36 inference(rectify,[status(thm)],[f2])).
% 1.69/1.36 thf(f2,negated_conjecture,(
% 1.69/1.36 ~! [X3 : a,X1 : a,X2 : a,X0 : a > a > $o] : ((! [X4 : a > $o] : ((! [X5 : a] : ((X0 @ X2 @ X5) => (X4 @ X5)) & ! [X7 : a,X6 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7))) => (X4 @ X3)) & ! [X4 : a > $o] : ((! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5)) & ! [X7 : a,X6 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7))) => (X4 @ X2))) => ! [X4 : a > $o] : ((! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5)) & ! [X6 : a,X7 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7))) => (X4 @ X3)))),
% 1.69/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.69/1.36 thf(f1,conjecture,(
% 1.69/1.36 ! [X3 : a,X1 : a,X2 : a,X0 : a > a > $o] : ((! [X4 : a > $o] : ((! [X5 : a] : ((X0 @ X2 @ X5) => (X4 @ X5)) & ! [X7 : a,X6 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7))) => (X4 @ X3)) & ! [X4 : a > $o] : ((! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5)) & ! [X7 : a,X6 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7))) => (X4 @ X2))) => ! [X4 : a > $o] : ((! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5)) & ! [X6 : a,X7 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7))) => (X4 @ X3)))),
% 1.69/1.36 file('/export/starexec/sandbox/tmp/tmp.oGq4bMr1yX/DTF2THF_24689.p',cTHM150_pme)).
% 1.69/1.36 thf(f162,plain,(
% 1.69/1.36 spl0_2 | spl0_3),
% 1.69/1.36 inference(avatar_split_clause,[status(thm)],[f156,f160,f80])).
% 1.69/1.36 thf(f80,definition,(
% 1.69/1.36 spl0_2 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $false)),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.69/1.36 thf(f156,plain,(
% 1.69/1.36 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))) = $false)),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.69/1.36 thf(f144,plain,(
% 1.69/1.36 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0))))))),
% 1.69/1.36 inference(not_proxy_clausification,[status(thm)],[f44])).
% 1.69/1.36 thf(f44,plain,(
% 1.69/1.36 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))))))),
% 1.69/1.36 inference(boolean_simplification,[status(thm)],[f43])).
% 1.69/1.36 thf(f43,plain,(
% 1.69/1.36 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0))))) => $false))),
% 1.69/1.36 inference(superposition,[status(thm)],[f37,f26])).
% 1.69/1.36 thf(f26,plain,(
% 1.69/1.36 ($false = (sK6 @ sK5))),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.69/1.36 thf(f37,plain,(
% 1.69/1.36 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (X1 @ Y0)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (X1 @ Y0))))) => (X1 @ sK5)))) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.69/1.36 thf(f36,plain,(
% 1.69/1.36 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK5))) @ X1) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f35])).
% 1.69/1.36 thf(f35,plain,(
% 1.69/1.36 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK5)))))),
% 1.69/1.36 inference(boolean_simplification,[status(thm)],[f34])).
% 1.69/1.36 thf(f34,plain,(
% 1.69/1.36 (($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK5))))) = $true)),
% 1.69/1.36 inference(backward_demodulation,[status(thm)],[f19,f33])).
% 1.69/1.36 thf(f33,plain,(
% 1.69/1.36 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK3)))))),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.69/1.36 thf(f19,plain,(
% 1.69/1.36 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK3)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK5))))))),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.69/1.36 thf(f121,plain,(
% 1.69/1.36 ~spl0_2),
% 1.69/1.36 inference(avatar_contradiction_clause,[status(thm)],[f120])).
% 1.69/1.36 thf(f120,plain,(
% 1.69/1.36 $false | ~spl0_2),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.69/1.36 thf(f116,plain,(
% 1.69/1.36 ($true = $false) | ~spl0_2),
% 1.69/1.36 inference(superposition,[status(thm)],[f113,f65])).
% 1.69/1.36 thf(f113,plain,(
% 1.69/1.36 ((((sK2 @ sK7 @ sK8) & (sK6 @ sK7)) => (sK6 @ sK8)) = $false) | ~spl0_2),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f112])).
% 1.69/1.36 thf(f112,plain,(
% 1.69/1.36 ($false = ((^[Y0 : a]: (((sK2 @ sK7 @ Y0) & (sK6 @ sK7)) => (sK6 @ Y0))) @ sK8)) | ~spl0_2),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f102])).
% 1.69/1.36 thf(f102,plain,(
% 1.69/1.36 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ sK7 @ Y0) & (sK6 @ sK7)) => (sK6 @ Y0))))) | ~spl0_2),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.69/1.36 thf(f97,plain,(
% 1.69/1.36 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ sK7)) | ~spl0_2),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f81])).
% 1.69/1.36 thf(f81,plain,(
% 1.69/1.36 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $false) | ~spl0_2),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.69/1.36 thf(f82,plain,(
% 1.69/1.36 spl0_1 | spl0_2),
% 1.69/1.36 inference(avatar_split_clause,[status(thm)],[f75,f80,f77])).
% 1.69/1.36 thf(f75,plain,(
% 1.69/1.36 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $false) | ((sK6 @ sK3) = $true)),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.69/1.36 thf(f61,plain,(
% 1.69/1.36 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) => (sK6 @ sK3)))),
% 1.69/1.36 inference(boolean_simplification,[status(thm)],[f60])).
% 1.69/1.36 thf(f60,plain,(
% 1.69/1.36 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & $true) => (sK6 @ sK3)) = $true)),
% 1.69/1.36 inference(superposition,[status(thm)],[f54,f41])).
% 1.69/1.36 thf(f41,plain,(
% 1.69/1.36 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))))),
% 1.69/1.36 inference(boolean_simplification,[status(thm)],[f40])).
% 1.69/1.36 thf(f40,plain,(
% 1.69/1.36 ($true = ($true & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))))))),
% 1.69/1.36 inference(backward_demodulation,[status(thm)],[f27,f39])).
% 1.69/1.36 thf(f54,plain,(
% 1.69/1.36 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) & (X1 @ Y0)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (X1 @ Y0))))) => (X1 @ sK3)))) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.69/1.36 thf(f53,plain,(
% 1.69/1.36 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK3))) @ X1) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f33])).
% 1.69/1.36 % SZS output end Proof for DTF2THF_24689
% 1.69/1.36 % (24797)------------------------------
% 1.69/1.36 % (24797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (24797)Termination reason: Refutation
% 1.69/1.36
% 1.69/1.36 % (24797)Memory used [KB]: 5756
% 1.69/1.36 % (24797)Time elapsed: 0.018 s
% 1.69/1.36 % (24797)Instructions burned: 40 (million)
% 1.69/1.36 % (24797)------------------------------
% 1.69/1.36 % (24797)------------------------------
% 1.69/1.36 % (24785)Success in time 0.052 s
%------------------------------------------------------------------------------