%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV046^5 : 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 : n020.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 09:40:09 AM UTC 2026
% Result : Theorem 1.81s 1.64s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 4
% Syntax : Number of formulae : 149 ( 39 unt; 0 typ; 3 def)
% Number of atoms : 1322 ( 161 equ; 0 cnn)
% Maximal formula atoms : 3 ( 8 avg)
% Number of connectives : 3855 ( 120 ~; 112 |; 143 &;2694 @)
% ( 3 <=>; 322 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 204 ( 204 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 10 con; 0-3 aty)
% ( 461 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 656 ( 491 ^; 165 !; 0 ?; 656 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a > b > b > $o ).
thf(func_def_21,type,
sK3: a > a > $o ).
thf(func_def_22,type,
sK4: a > b ).
thf(func_def_23,type,
sK5: a > b ).
thf(func_def_24,type,
sK6: a > b ).
thf(func_def_25,type,
sK7: a > b ).
thf(func_def_26,type,
sK8: a ).
thf(func_def_27,type,
sK9: a ).
thf(func_def_28,type,
sK10: a > b ).
thf(func_def_29,type,
sK11: a > b ).
thf(func_def_30,type,
sK12: a ).
thf(func_def_31,type,
sK13: a ).
thf(f1151,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f42,f820,f849,f1150]) ).
thf(f1150,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f1149]) ).
thf(f1149,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1148]) ).
thf(f1148,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1147]) ).
thf(f1147,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f1138,f1036]) ).
thf(f1036,plain,
( ( $true
= ( sK2 @ sK12 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f882,f1016]) ).
thf(f1016,plain,
( ! [X2: b,X1: b] :
( ( sK2 @ sK13 @ X1 @ X2 )
= ( sK2 @ sK12 @ X1 @ X2 ) )
| ~ spl0_1 ),
inference(argument_congruence,[status(thm)],[f1013]) ).
thf(f1013,plain,
( ! [X1: b] :
( ( sK2 @ sK13 @ X1 )
= ( sK2 @ sK12 @ X1 ) )
| ~ spl0_1 ),
inference(argument_congruence,[status(thm)],[f1006]) ).
thf(f1006,plain,
( ( ( sK2 @ sK12 )
= ( sK2 @ sK13 ) )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f858]) ).
thf(f858,plain,
( ( $true
= ( ( sK2 @ sK13 )
= ( sK2 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f855]) ).
thf(f855,plain,
( ( $true
= ( $true
=> ( ( sK2 @ sK13 )
= ( sK2 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f195,f836]) ).
thf(f836,plain,
( ( $true
= ( sK3 @ sK12 @ sK13 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f834]) ).
thf(f834,plain,
( ( ( ( sK3 @ sK12 @ sK13 )
=> ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f833]) ).
thf(f833,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ Y0 ) ) )
@ sK13 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f832]) ).
thf(f832,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f831]) ).
thf(f831,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f830]) ).
thf(f830,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f829]) ).
thf(f829,plain,
( ( ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f826,f828]) ).
thf(f828,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK10 @ Y0 ) @ ( sK11 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f826]) ).
thf(f826,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK10 @ Y0 ) @ ( sK11 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f825]) ).
thf(f825,plain,
( ( ( ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK10 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK10 @ Y2 ) ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f824]) ).
thf(f824,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK10 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK10 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f823]) ).
thf(f823,plain,
( ( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_1
<=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f195,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( ( sK2 @ X2 )
= ( sK2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f194]) ).
thf(f194,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( ( sK2 @ Y0 )
= ( sK2 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( ( sK2 @ Y0 )
= ( sK2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f190]) ).
thf(f190,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f186]) ).
thf(f186,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f32,f184]) ).
thf(f184,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y1 )
& ( sK2 @ Y0 @ Y1 @ Y3 ) )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y1 )
& ( sK2 @ Y0 @ Y1 @ Y3 ) )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y1 )
& ( sK2 @ Y0 @ Y1 @ Y3 ) )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y1 )
& ( sK2 @ Y0 @ Y1 @ Y3 ) )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y1 )
& ( sK2 @ Y0 @ Y1 @ Y3 ) )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( ( sK2 @ Y2 )
= ( sK2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y1 @ Y3 @ Y2 )
& ( sK2 @ Y1 @ Y2 @ Y4 ) )
=> ( sK2 @ Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y1 @ Y3 @ Y2 )
=> ( sK2 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( sK2 @ Y5 @ ( Y3 @ Y5 ) @ ( Y2 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( ( sK2 @ Y2 )
= ( sK2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y1 @ Y3 @ Y2 )
& ( sK2 @ Y1 @ Y2 @ Y4 ) )
=> ( sK2 @ Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y1 @ Y3 @ Y2 )
=> ( sK2 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( sK2 @ Y5 @ ( Y3 @ Y5 ) @ ( Y2 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y3 @ Y5 ) )
=> ( Y0 @ Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y4 @ Y3 )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y0 @ Y6 @ ( Y4 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y3 @ Y5 ) )
=> ( Y0 @ Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y4 @ Y3 )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y0 @ Y6 @ ( Y4 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y3 @ Y5 ) )
=> ( Y0 @ Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y4 @ Y3 )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y0 @ Y6 @ ( Y4 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y3 @ Y5 ) )
=> ( Y0 @ Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y4 @ Y3 )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y0 @ Y6 @ ( Y4 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > b > b > $o] :
( ( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X2 @ X4 ) )
=> ( X0 @ X3 @ X4 ) )
& ! [X5: a,X6: a] :
( ( X0 @ X6 @ X5 )
=> ( X0 @ X5 @ X6 ) )
& ! [X7: a] :
( ( X0 @ X7 @ X7 )
=> ( ! [X8: b,X9: b] :
( ( X1 @ X7 @ X8 @ X9 )
=> ( X1 @ X7 @ X9 @ X8 ) )
& ! [X10: b,X11: b,X12: b] :
( ( ( X1 @ X7 @ X12 @ X10 )
& ( X1 @ X7 @ X11 @ X12 ) )
=> ( X1 @ X7 @ X11 @ X10 ) ) ) )
& ! [X13: a,X14: a] :
( ( X0 @ X14 @ X13 )
=> ( ( X1 @ X13 )
= ( X1 @ X14 ) ) ) )
=> ( ! [X15: a > b,X16: a > b,X17: a > b] :
( ( ! [X18: a,X19: a] :
( ( X0 @ X18 @ X19 )
=> ( X1 @ X18 @ ( X15 @ X18 ) @ ( X16 @ X19 ) ) )
& ! [X20: a,X21: a] :
( ( X0 @ X21 @ X20 )
=> ( X1 @ X21 @ ( X17 @ X21 ) @ ( X15 @ X20 ) ) ) )
=> ! [X22: a,X23: a] :
( ( X0 @ X23 @ X22 )
=> ( X1 @ X23 @ ( X17 @ X23 ) @ ( X16 @ X22 ) ) ) )
& ! [X24: a > b,X25: a > b] :
( ! [X26: a,X27: a] :
( ( X0 @ X27 @ X26 )
=> ( X1 @ X27 @ ( X25 @ X27 ) @ ( X24 @ X26 ) ) )
=> ! [X28: a,X29: a] :
( ( X0 @ X29 @ X28 )
=> ( X1 @ X29 @ ( X24 @ X29 ) @ ( X25 @ X28 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > b > b > $o] :
( ( ! [X3: a,X2: a,X4: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
=> ( ! [X5: b,X3: b] :
( ( X1 @ X2 @ X5 @ X3 )
=> ( X1 @ X2 @ X3 @ X5 ) )
& ! [X4: b,X5: b,X3: b] :
( ( ( X1 @ X2 @ X3 @ X4 )
& ( X1 @ X2 @ X5 @ X3 ) )
=> ( X1 @ X2 @ X5 @ X4 ) ) ) )
& ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( ( X1 @ X2 )
= ( X1 @ X3 ) ) ) )
=> ( ! [X3: a > b,X4: a > b,X2: a > b] :
( ( ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) )
& ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) ) )
=> ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X4 @ X6 ) ) ) )
& ! [X3: a > b,X2: a > b] :
( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) )
=> ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X2 @ X6 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > b > b > $o] :
( ( ! [X3: a,X2: a,X4: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
=> ( ! [X5: b,X3: b] :
( ( X1 @ X2 @ X5 @ X3 )
=> ( X1 @ X2 @ X3 @ X5 ) )
& ! [X4: b,X5: b,X3: b] :
( ( ( X1 @ X2 @ X3 @ X4 )
& ( X1 @ X2 @ X5 @ X3 ) )
=> ( X1 @ X2 @ X5 @ X4 ) ) ) )
& ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( ( X1 @ X2 )
= ( X1 @ X3 ) ) ) )
=> ( ! [X3: a > b,X4: a > b,X2: a > b] :
( ( ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) )
& ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) ) )
=> ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X4 @ X6 ) ) ) )
& ! [X3: a > b,X2: a > b] :
( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) )
=> ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X2 @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kat0iVf5Pk/DTF2THF_3007.p',cTHM507_pme) ).
thf(f882,plain,
( ( $true
= ( sK2 @ sK13 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f880]) ).
thf(f880,plain,
( ( $true
= ( $true
=> ( sK2 @ sK13 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f877,f856]) ).
thf(f856,plain,
( ( $true
= ( sK3 @ sK13 @ sK12 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f853]) ).
thf(f853,plain,
( ( $true
= ( $true
=> ( sK3 @ sK13 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f50,f836]) ).
thf(f50,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( sK3 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK3 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK3 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f21,f32]) ).
thf(f877,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( sK2 @ X1 @ ( sK10 @ X1 ) @ ( sK11 @ X2 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f876]) ).
thf(f876,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK10 @ X1 ) @ ( sK11 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f863]) ).
thf(f863,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK10 @ X1 ) @ ( sK11 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f862]) ).
thf(f862,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK10 @ Y0 ) @ ( sK11 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f828]) ).
thf(f1138,plain,
( ( $true
= ( ~ ( sK2 @ sK12 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1124]) ).
thf(f1124,plain,
( ( $true
= ( ( sK2 @ sK12 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f1089,f844]) ).
thf(f844,plain,
( ( $false
= ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f843]) ).
thf(f843,definition,
( spl0_4
<=> ( $false
= ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1089,plain,
( ! [X2: b,X1: b] :
( $true
= ( ( sK2 @ sK12 @ X2 @ X1 )
=> ( sK2 @ sK12 @ X1 @ X2 ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1088,f1016]) ).
thf(f1088,plain,
( ! [X2: b,X1: b] :
( $true
= ( ( sK2 @ sK12 @ X2 @ X1 )
=> ( sK2 @ sK13 @ X1 @ X2 ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1087,f1016]) ).
thf(f1087,plain,
( ! [X2: b,X1: b] :
( $true
= ( ( sK2 @ sK13 @ X2 @ X1 )
=> ( sK2 @ sK13 @ X1 @ X2 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f1086]) ).
thf(f1086,plain,
( ! [X2: b,X1: b] :
( $true
= ( ^ [Y0: b] :
( ( sK2 @ sK13 @ Y0 @ X1 )
=> ( sK2 @ sK13 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f1078]) ).
thf(f1078,plain,
( ! [X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( ( sK2 @ sK13 @ Y0 @ X1 )
=> ( sK2 @ sK13 @ X1 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f1075]) ).
thf(f1075,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK13 @ Y1 @ Y0 )
=> ( sK2 @ sK13 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f1050]) ).
thf(f1050,plain,
( ( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK13 @ Y1 @ Y0 )
=> ( sK2 @ sK13 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f911]) ).
thf(f911,plain,
( ( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK13 @ Y1 @ Y0 )
& ( sK2 @ sK13 @ Y0 @ Y2 ) )
=> ( sK2 @ sK13 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK13 @ Y1 @ Y0 )
=> ( sK2 @ sK13 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f897]) ).
thf(f897,plain,
( ( $true
= ( $true
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK13 @ Y1 @ Y0 )
& ( sK2 @ sK13 @ Y0 @ Y2 ) )
=> ( sK2 @ sK13 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK13 @ Y1 @ Y0 )
=> ( sK2 @ sK13 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f253,f894]) ).
thf(f894,plain,
( ( $true
= ( sK3 @ sK13 @ sK13 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f890]) ).
thf(f890,plain,
( ( $true
= ( $true
=> ( sK3 @ sK13 @ sK13 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f857,f856]) ).
thf(f857,plain,
( ! [X0: a] :
( $true
= ( ( sK3 @ X0 @ sK12 )
=> ( sK3 @ X0 @ sK13 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f850]) ).
thf(f850,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK3 @ X0 @ sK12 ) )
=> ( sK3 @ X0 @ sK13 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f29,f836]) ).
thf(f29,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK3 @ X3 @ X1 )
& ( sK3 @ X2 @ X3 ) )
=> ( sK3 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ X1 )
& ( sK3 @ X2 @ Y0 ) )
=> ( sK3 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ X1 )
& ( sK3 @ X2 @ Y0 ) )
=> ( sK3 @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ X1 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ X1 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f15,f21]) ).
thf(f253,plain,
! [X1: a] :
( $true
= ( ( sK3 @ X1 @ X1 )
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ X1 @ Y1 @ Y0 )
& ( sK2 @ X1 @ Y0 @ Y2 ) )
=> ( sK2 @ X1 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ X1 @ Y1 @ Y0 )
=> ( sK2 @ X1 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f252]) ).
thf(f252,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y1 )
& ( sK2 @ Y0 @ Y1 @ Y3 ) )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f184]) ).
thf(f849,plain,
( spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f848,f37,f843]) ).
thf(f848,plain,
( ( $false
= ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f847]) ).
thf(f847,plain,
( ( $false
= ( $true
=> ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f834,f836]) ).
thf(f820,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f819]) ).
thf(f819,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f818]) ).
thf(f818,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f817]) ).
thf(f817,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f808,f180]) ).
thf(f180,plain,
( ( $true
= ( sK2 @ sK8 @ ( sK6 @ sK8 ) @ ( sK5 @ sK9 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f178]) ).
thf(f178,plain,
( ( $true
= ( $true
=> ( sK2 @ sK8 @ ( sK6 @ sK8 ) @ ( sK5 @ sK9 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f172,f78]) ).
thf(f78,plain,
( ( $true
= ( sK3 @ sK8 @ sK9 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( ( sK3 @ sK8 @ sK9 )
=> ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ ( sK5 @ sK9 ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ ( sK5 @ Y0 ) ) )
@ sK9 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ ( sK5 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ Y1 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK6 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $false
= ( ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK2 @ Y2 @ ( Y0 @ Y2 ) @ ( sK5 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
@ sK6 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK2 @ Y2 @ ( Y0 @ Y2 ) @ ( sK5 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) )
@ sK5 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) )
@ sK4 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl0_2
<=> ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f172,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X2 @ X1 )
=> ( sK2 @ X2 @ ( sK6 @ X2 ) @ ( sK5 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK2 @ Y0 @ ( sK6 @ Y0 ) @ ( sK5 @ X1 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK2 @ Y0 @ ( sK6 @ Y0 ) @ ( sK5 @ X1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f167]) ).
thf(f167,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK6 @ Y1 ) @ ( sK5 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK6 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK6 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f808,plain,
( ( ( ~ ( sK2 @ sK8 @ ( sK6 @ sK8 ) @ ( sK5 @ sK9 ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f798]) ).
thf(f798,plain,
( ( $true
= ( ( sK2 @ sK8 @ ( sK6 @ sK8 ) @ ( sK5 @ sK9 ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f546,f80]) ).
thf(f80,plain,
( ( ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ ( sK5 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( $true
=> ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ ( sK5 @ sK9 ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f72,f78]) ).
thf(f546,plain,
( ! [X0: b] :
( $true
= ( ( sK2 @ sK8 @ ( sK6 @ sK8 ) @ X0 )
=> ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ X0 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f536]) ).
thf(f536,plain,
( ! [X0: b] :
( $true
= ( ( $true
& ( sK2 @ sK8 @ ( sK6 @ sK8 ) @ X0 ) )
=> ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ X0 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f477,f163]) ).
thf(f163,plain,
( ( $true
= ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ ( sK6 @ sK8 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f160]) ).
thf(f160,plain,
( ( $true
= ( $true
=> ( sK2 @ sK8 @ ( sK4 @ sK8 ) @ ( sK6 @ sK8 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f139,f136]) ).
thf(f136,plain,
( ( $true
= ( sK3 @ sK8 @ sK8 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true
= ( $true
=> ( sK3 @ sK8 @ sK8 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f89,f91]) ).
thf(f91,plain,
( ( $true
= ( sK3 @ sK9 @ sK8 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true
= ( $true
=> ( sK3 @ sK9 @ sK8 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f50,f78]) ).
thf(f89,plain,
( ! [X0: a] :
( $true
= ( ( sK3 @ sK9 @ X0 )
=> ( sK3 @ sK8 @ X0 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f86]) ).
thf(f86,plain,
( ! [X0: a] :
( $true
= ( ( ( sK3 @ sK9 @ X0 )
& $true )
=> ( sK3 @ sK8 @ X0 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f29,f78]) ).
thf(f139,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK6 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f138]) ).
thf(f138,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK6 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK6 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f57,f125]) ).
thf(f477,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK2 @ sK8 @ X2 @ X1 )
& ( sK2 @ sK8 @ X1 @ X3 ) )
=> ( sK2 @ sK8 @ X2 @ X3 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f476]) ).
thf(f476,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ^ [Y0: b] :
( ( ( sK2 @ sK8 @ X2 @ X1 )
& ( sK2 @ sK8 @ X1 @ Y0 ) )
=> ( sK2 @ sK8 @ X2 @ Y0 ) )
@ X3 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f471]) ).
thf(f471,plain,
( ! [X2: b,X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( ( ( sK2 @ sK8 @ X2 @ X1 )
& ( sK2 @ sK8 @ X1 @ Y0 ) )
=> ( sK2 @ sK8 @ X2 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f470]) ).
thf(f470,plain,
( ! [X2: b,X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK2 @ sK8 @ Y0 @ X1 )
& ( sK2 @ sK8 @ X1 @ Y1 ) )
=> ( sK2 @ sK8 @ Y0 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f462]) ).
thf(f462,plain,
( ! [X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK2 @ sK8 @ Y0 @ X1 )
& ( sK2 @ sK8 @ X1 @ Y1 ) )
=> ( sK2 @ sK8 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f460]) ).
thf(f460,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK8 @ Y1 @ Y0 )
& ( sK2 @ sK8 @ Y0 @ Y2 ) )
=> ( sK2 @ sK8 @ Y1 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f455]) ).
thf(f455,plain,
( ( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK8 @ Y1 @ Y0 )
& ( sK2 @ sK8 @ Y0 @ Y2 ) )
=> ( sK2 @ sK8 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f454]) ).
thf(f454,plain,
( ( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK8 @ Y1 @ Y0 )
& ( sK2 @ sK8 @ Y0 @ Y2 ) )
=> ( sK2 @ sK8 @ Y1 @ Y2 ) ) ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f260,f450]) ).
thf(f450,plain,
( ( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK8 @ Y1 @ Y0 )
=> ( sK2 @ sK8 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f260]) ).
thf(f260,plain,
( ( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK8 @ Y1 @ Y0 )
& ( sK2 @ sK8 @ Y0 @ Y2 ) )
=> ( sK2 @ sK8 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK8 @ Y1 @ Y0 )
=> ( sK2 @ sK8 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( $true
= ( $true
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK8 @ Y1 @ Y0 )
& ( sK2 @ sK8 @ Y0 @ Y2 ) )
=> ( sK2 @ sK8 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK8 @ Y1 @ Y0 )
=> ( sK2 @ sK8 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f253,f136]) ).
thf(f42,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f35,f40,f37]) ).
thf(f35,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV046^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n020.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:39:27 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.41 ---- Original DTF file ---
% 0.17/0.41 thf(spec,logic,$$dhol).
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 % File : SEV046^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.41 % Domain : Set Theory (Relations)
% 0.17/0.41 % Problem : TPS problem from PERS-THMS
% 0.17/0.41 % Version : Especial.
% 0.17/0.41 % English :
% 0.17/0.41
% 0.17/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.41 % Source : [Bro09]
% 0.17/0.41 % Names : tps_1181 [Bro09]
% 0.17/0.41
% 0.17/0.41 % Status : Theorem
% 0.17/0.41 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.33 v4.0.1, 1.00 v4.0.0
% 0.17/0.41 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.17/0.41 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.17/0.41 % Maximal formula atoms : 1 ( 1 avg)
% 0.17/0.41 % Number of connectives : 88 ( 0 ~; 0 |; 8 &; 66 @)
% 0.17/0.41 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.17/0.41 % Maximal formula depth : 18 ( 18 avg)
% 0.17/0.41 % Number of types : 3 ( 2 usr)
% 0.17/0.41 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.17/0.41 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.17/0.41 % Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% 0.17/0.41 % SPC : TH0_THM_EQU_NAR
% 0.17/0.41
% 0.17/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 thf(a_type,type,
% 0.17/0.41 a: $tType ).
% 0.17/0.41
% 0.17/0.41 thf(b_type,type,
% 0.17/0.41 b: $tType ).
% 0.17/0.41
% 0.17/0.41 thf(cTHM507_pme,conjecture,
% 0.17/0.41 ! [Xp: a > a > $o,Xp2: a > b > b > $o] :
% 0.17/0.41 ( ( ! [Xx: a,Xy: a] :
% 0.17/0.41 ( ( Xp @ Xx @ Xy )
% 0.17/0.41 => ( Xp @ Xy @ Xx ) )
% 0.17/0.41 & ! [Xx: a,Xy: a,Xz: a] :
% 0.17/0.41 ( ( ( Xp @ Xx @ Xy )
% 0.17/0.41 & ( Xp @ Xy @ Xz ) )
% 0.17/0.41 => ( Xp @ Xx @ Xz ) )
% 0.17/0.41 & ! [Xx: a] :
% 0.17/0.41 ( ( Xp @ Xx @ Xx )
% 0.17/0.41 => ( ! [Xx0: b,Xy: b] :
% 0.17/0.41 ( ( Xp2 @ Xx @ Xx0 @ Xy )
% 0.17/0.41 => ( Xp2 @ Xx @ Xy @ Xx0 ) )
% 0.17/0.41 & ! [Xx0: b,Xy: b,Xz: b] :
% 0.17/0.41 ( ( ( Xp2 @ Xx @ Xx0 @ Xy )
% 0.17/0.41 & ( Xp2 @ Xx @ Xy @ Xz ) )
% 0.17/0.41 => ( Xp2 @ Xx @ Xx0 @ Xz ) ) ) )
% 0.17/0.41 & ! [Xx: a,Xy: a] :
% 0.17/0.41 ( ( Xp @ Xx @ Xy )
% 0.17/0.41 => ( ( Xp2 @ Xx )
% 0.17/0.41 = ( Xp2 @ Xy ) ) ) )
% 0.17/0.41 => ( ! [Xx: a > b,Xy: a > b] :
% 0.17/0.41 ( ! [Xx0: a,Xy0: a] :
% 0.17/0.41 ( ( Xp @ Xx0 @ Xy0 )
% 0.17/0.41 => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
% 0.17/0.41 => ! [Xx0: a,Xy0: a] :
% 0.17/0.41 ( ( Xp @ Xx0 @ Xy0 )
% 0.17/0.41 => ( Xp2 @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) )
% 0.17/0.41 & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
% 0.17/0.41 ( ( ! [Xx0: a,Xy0: a] :
% 0.17/0.41 ( ( Xp @ Xx0 @ Xy0 )
% 0.17/0.41 => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
% 0.17/0.41 & ! [Xx0: a,Xy0: a] :
% 0.17/0.41 ( ( Xp @ Xx0 @ Xy0 )
% 0.17/0.41 => ( Xp2 @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
% 0.17/0.41 => ! [Xx0: a,Xy0: a] :
% 0.17/0.41 ( ( Xp @ Xx0 @ Xy0 )
% 0.17/0.41 => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 ------------------------
% 1.73/1.43 ---- Embedded in THF ---
% 1.73/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.73/1.43 %%% Generated on Tue Feb 24 12:39:28 EST 2026
% 1.73/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.73/1.43 %%% Logic specification used:
% 1.73/1.43 %%% thf(spec, logic, $$dhol).
% 1.73/1.43
% 1.73/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kat0iVf5Pk/DTF2DTF3007.p
% See solution above
% 1.73/1.43 ------------------------
% 1.73/1.44 ---- Cleaned THF ---
% 1.73/1.44 thf(a_type,type,
% 1.73/1.44 a: $tType ).
% 1.73/1.44
% 1.73/1.44 thf(b_type,type,
% 1.73/1.44 b: $tType ).
% 1.73/1.44
% 1.73/1.44 thf(cTHM507_pme,conjecture,
% 1.73/1.44 ! [Xp: a > a > $o,Xp2: a > b > b > $o] :
% 1.73/1.44 ( ( ! [Xx: a,Xy: a] :
% 1.73/1.44 ( ( Xp @ Xx @ Xy )
% 1.73/1.44 => ( Xp @ Xy @ Xx ) )
% 1.73/1.44 & ! [Xx: a,Xy: a,Xz: a] :
% 1.73/1.44 ( ( ( Xp @ Xx @ Xy )
% 1.73/1.44 & ( Xp @ Xy @ Xz ) )
% 1.73/1.44 => ( Xp @ Xx @ Xz ) )
% 1.73/1.44 & ! [Xx: a] :
% 1.73/1.44 ( ( Xp @ Xx @ Xx )
% 1.73/1.44 => ( ! [Xx0: b,Xy: b] :
% 1.73/1.44 ( ( Xp2 @ Xx @ Xx0 @ Xy )
% 1.73/1.44 => ( Xp2 @ Xx @ Xy @ Xx0 ) )
% 1.73/1.44 & ! [Xx0: b,Xy: b,Xz: b] :
% 1.73/1.44 ( ( ( Xp2 @ Xx @ Xx0 @ Xy )
% 1.73/1.44 & ( Xp2 @ Xx @ Xy @ Xz ) )
% 1.73/1.44 => ( Xp2 @ Xx @ Xx0 @ Xz ) ) ) )
% 1.73/1.44 & ! [Xx: a,Xy: a] :
% 1.73/1.44 ( ( Xp @ Xx @ Xy )
% 1.73/1.44 => ( ( Xp2 @ Xx )
% 1.73/1.44 = ( Xp2 @ Xy ) ) ) )
% 1.73/1.44 => ( ! [Xx: a > b,Xy: a > b] :
% 1.73/1.44 ( ! [Xx0: a,Xy0: a] :
% 1.73/1.44 ( ( Xp @ Xx0 @ Xy0 )
% 1.73/1.44 => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
% 1.73/1.44 => ! [Xx0: a,Xy0: a] :
% 1.73/1.44 ( ( Xp @ Xx0 @ Xy0 )
% 1.73/1.44 => ( Xp2 @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) )
% 1.73/1.44 & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
% 1.73/1.44 ( ( ! [Xx0: a,Xy0: a] :
% 1.73/1.44 ( ( Xp @ Xx0 @ Xy0 )
% 1.73/1.44 => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
% 1.73/1.44 & ! [Xx0: a,Xy0: a] :
% 1.73/1.44 ( ( Xp @ Xx0 @ Xy0 )
% 1.73/1.44 => ( Xp2 @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
% 1.73/1.44 => ! [Xx0: a,Xy0: a] :
% 1.73/1.44 ( ( Xp @ Xx0 @ Xy0 )
% 1.73/1.44 => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) ) ).
% 1.73/1.44 ------------------------
% 1.73/1.46 % (3106)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_3007 for (2999ds/4Mi)
% 1.73/1.46 % (3111)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/18Mi)
% 1.73/1.46 % (3108)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/2Mi)
% 1.73/1.46 % (3109)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_3007 for (2999ds/2Mi)
% 1.73/1.46 % (3108)Instruction limit reached!
% 1.73/1.46 % (3108)------------------------------
% 1.73/1.46 % (3108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.46 % (3108)Termination reason: Unknown
% 1.73/1.46 % (3108)Termination phase: Property scanning
% 1.73/1.46
% 1.73/1.46 % (3108)Memory used [KB]: 895
% 1.73/1.46 % (3109)Instruction limit reached!
% 1.73/1.46 % (3109)------------------------------
% 1.73/1.46 % (3109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.46 % (3109)Termination reason: Unknown
% 1.73/1.46 % (3109)Termination phase: shuffling
% 1.73/1.46
% 1.73/1.46 % (3109)Memory used [KB]: 895
% 1.73/1.46 % (3109)Time elapsed: 0.002 s
% 1.73/1.46 % (3109)Instructions burned: 2 (million)
% 1.73/1.46 % (3109)------------------------------
% 1.73/1.46 % (3109)------------------------------
% 1.73/1.46 % (3108)Time elapsed: 0.002 s
% 1.73/1.46 % (3108)Instructions burned: 2 (million)
% 1.73/1.46 % (3108)------------------------------
% 1.73/1.46 % (3108)------------------------------
% 1.73/1.46 % (3107)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_3007 for (2999ds/27Mi)
% 1.73/1.46 % (3106)Instruction limit reached!
% 1.73/1.46 % (3106)------------------------------
% 1.73/1.46 % (3106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.46 % (3106)Termination reason: Unknown
% 1.73/1.46 % (3106)Termination phase: Property scanning
% 1.73/1.46
% 1.73/1.46 % (3106)Memory used [KB]: 1023
% 1.73/1.46 % (3106)Time elapsed: 0.004 s
% 1.73/1.46 % (3106)Instructions burned: 4 (million)
% 1.73/1.46 % (3106)------------------------------
% 1.73/1.46 % (3106)------------------------------
% 1.73/1.46 % (3110)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_3007 for (2999ds/275Mi)
% 1.73/1.47 % (3105)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/183Mi)
% 1.73/1.47 % (3111)Instruction limit reached!
% 1.73/1.47 % (3111)------------------------------
% 1.73/1.47 % (3111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.47 % (3111)Termination reason: Unknown
% 1.73/1.47 % (3111)Termination phase: Saturation
% 1.73/1.47
% 1.73/1.47 % (3111)Memory used [KB]: 5628
% 1.73/1.47 % (3111)Time elapsed: 0.013 s
% 1.73/1.47 % (3111)Instructions burned: 19 (million)
% 1.73/1.47 % (3111)------------------------------
% 1.73/1.47 % (3111)------------------------------
% 1.73/1.48 % (3107)Instruction limit reached!
% 1.73/1.48 % (3107)------------------------------
% 1.73/1.48 % (3107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.48 % (3107)Termination reason: Unknown
% 1.73/1.48 % (3107)Termination phase: Saturation
% 1.73/1.48
% 1.73/1.48 % (3107)Memory used [KB]: 5628
% 1.73/1.48 % (3107)Time elapsed: 0.017 s
% 1.73/1.48 % (3107)Instructions burned: 27 (million)
% 1.73/1.48 % (3107)------------------------------
% 1.73/1.48 % (3107)------------------------------
% 1.73/1.48 % (3113)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_3007 for (2999ds/37Mi)
% 1.73/1.48 % (3114)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_3007 for (2999ds/15Mi)
% 1.73/1.48 % (3112)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/3Mi)
% 1.73/1.48 % (3112)Instruction limit reached!
% 1.73/1.48 % (3112)------------------------------
% 1.73/1.48 % (3112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.48 % (3112)Termination reason: Unknown
% 1.73/1.48 % (3112)Termination phase: Property scanning
% 1.73/1.48
% 1.73/1.48 % (3112)Memory used [KB]: 1023
% 1.73/1.48 % (3112)Time elapsed: 0.003 s
% 1.73/1.48 % (3112)Instructions burned: 4 (million)
% 1.73/1.48 % (3112)------------------------------
% 1.73/1.48 % (3112)------------------------------
% 1.73/1.49 % (3114)Instruction limit reached!
% 1.73/1.49 % (3114)------------------------------
% 1.73/1.49 % (3114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.49 % (3114)Termination reason: Unknown
% 1.73/1.49 % (3114)Termination phase: Saturation
% 1.73/1.49
% 1.73/1.49 % (3114)Memory used [KB]: 5628
% 1.73/1.49 % (3114)Time elapsed: 0.010 s
% 1.73/1.49 % (3114)Instructions burned: 16 (million)
% 1.73/1.49 % (3114)------------------------------
% 1.73/1.49 % (3114)------------------------------
% 1.73/1.49 % (3115)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_3007 for (2999ds/3Mi)
% 1.73/1.49 % (3115)Instruction limit reached!
% 1.73/1.49 % (3115)------------------------------
% 1.73/1.49 % (3115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.49 % (3115)Termination reason: Unknown
% 1.73/1.49 % (3115)Termination phase: Saturation
% 1.73/1.49
% 1.73/1.49 % (3115)Memory used [KB]: 5500
% 1.73/1.49 % (3115)Time elapsed: 0.004 s
% 1.73/1.49 % (3115)Instructions burned: 4 (million)
% 1.73/1.49 % (3115)------------------------------
% 1.73/1.49 % (3115)------------------------------
% 1.81/1.50 % (3117)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/7Mi)
% 1.81/1.50 % (3116)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_3007 for (2999ds/1041Mi)
% 1.81/1.50 % (3113)Instruction limit reached!
% 1.81/1.50 % (3113)------------------------------
% 1.81/1.50 % (3113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.50 % (3113)Termination reason: Unknown
% 1.81/1.50 % (3113)Termination phase: Saturation
% 1.81/1.50
% 1.81/1.50 % (3113)Memory used [KB]: 5756
% 1.81/1.50 % (3113)Time elapsed: 0.021 s
% 1.81/1.50 % (3113)Instructions burned: 37 (million)
% 1.81/1.50 % (3113)------------------------------
% 1.81/1.50 % (3113)------------------------------
% 1.81/1.50 % (3117)Instruction limit reached!
% 1.81/1.50 % (3117)------------------------------
% 1.81/1.50 % (3117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.50 % (3117)Termination reason: Unknown
% 1.81/1.50 % (3117)Termination phase: Saturation
% 1.81/1.50
% 1.81/1.50 % (3117)Memory used [KB]: 1023
% 1.81/1.50 % (3117)Time elapsed: 0.006 s
% 1.81/1.50 % (3117)Instructions burned: 7 (million)
% 1.81/1.50 % (3117)------------------------------
% 1.81/1.50 % (3117)------------------------------
% 1.81/1.51 % (3118)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/16Mi)
% 1.81/1.51 % (3119)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_3007 for (2999ds/3Mi)
% 1.81/1.51 % (3119)Instruction limit reached!
% 1.81/1.51 % (3119)------------------------------
% 1.81/1.51 % (3119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.51 % (3119)Termination reason: Unknown
% 1.81/1.51 % (3119)Termination phase: Preprocessing 3
% 1.81/1.51
% 1.81/1.51 % (3119)Memory used [KB]: 1023
% 1.81/1.51 % (3119)Time elapsed: 0.004 s
% 1.81/1.51 % (3119)Instructions burned: 3 (million)
% 1.81/1.51 % (3119)------------------------------
% 1.81/1.51 % (3119)------------------------------
% 1.81/1.51 % (3118)Instruction limit reached!
% 1.81/1.51 % (3118)------------------------------
% 1.81/1.51 % (3118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.51 % (3118)Termination reason: Unknown
% 1.81/1.51 % (3118)Termination phase: Saturation
% 1.81/1.51
% 1.81/1.51 % (3118)Memory used [KB]: 5756
% 1.81/1.51 % (3118)Time elapsed: 0.011 s
% 1.81/1.51 % (3118)Instructions burned: 16 (million)
% 1.81/1.51 % (3118)------------------------------
% 1.81/1.51 % (3118)------------------------------
% 1.81/1.52 % (3120)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_3007 for (2999ds/3Mi)
% 1.81/1.52 % (3120)Instruction limit reached!
% 1.81/1.52 % (3120)------------------------------
% 1.81/1.52 % (3120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (3120)Termination reason: Unknown
% 1.81/1.52 % (3120)Termination phase: Preprocessing 3
% 1.81/1.52
% 1.81/1.52 % (3120)Memory used [KB]: 1023
% 1.81/1.52 % (3120)Time elapsed: 0.003 s
% 1.81/1.52 % (3120)Instructions burned: 3 (million)
% 1.81/1.52 % (3120)------------------------------
% 1.81/1.52 % (3120)------------------------------
% 1.81/1.52 % (3121)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/7Mi)
% 1.81/1.52 % (3121)Instruction limit reached!
% 1.81/1.52 % (3121)------------------------------
% 1.81/1.52 % (3121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (3121)Termination reason: Unknown
% 1.81/1.52 % (3121)Termination phase: Saturation
% 1.81/1.52
% 1.81/1.52 % (3121)Memory used [KB]: 5628
% 1.81/1.52 % (3121)Time elapsed: 0.006 s
% 1.81/1.52 % (3121)Instructions burned: 8 (million)
% 1.81/1.52 % (3121)------------------------------
% 1.81/1.52 % (3121)------------------------------
% 1.81/1.53 % (3122)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/3Mi)
% 1.81/1.53 % (3122)Instruction limit reached!
% 1.81/1.53 % (3122)------------------------------
% 1.81/1.53 % (3122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.53 % (3122)Termination reason: Unknown
% 1.81/1.53 % (3122)Termination phase: Property scanning
% 1.81/1.53
% 1.81/1.53 % (3122)Memory used [KB]: 1023
% 1.81/1.53 % (3122)Time elapsed: 0.003 s
% 1.81/1.53 % (3122)Instructions burned: 3 (million)
% 1.81/1.53 % (3122)------------------------------
% 1.81/1.53 % (3122)------------------------------
% 1.81/1.53 % (3123)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/4Mi)
% 1.81/1.53 % (3124)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/18Mi)
% 1.81/1.53 % (3123)Instruction limit reached!
% 1.81/1.53 % (3123)------------------------------
% 1.81/1.53 % (3123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.53 % (3123)Termination reason: Unknown
% 1.81/1.53 % (3123)Termination phase: Preprocessing 3
% 1.81/1.53
% 1.81/1.53 % (3123)Memory used [KB]: 1023
% 1.81/1.53 % (3123)Time elapsed: 0.004 s
% 1.81/1.53 % (3123)Instructions burned: 4 (million)
% 1.81/1.53 % (3123)------------------------------
% 1.81/1.53 % (3123)------------------------------
% 1.81/1.54 % (3125)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/710Mi)
% 1.81/1.54 % (3124)Instruction limit reached!
% 1.81/1.54 % (3124)------------------------------
% 1.81/1.54 % (3124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.54 % (3124)Termination reason: Unknown
% 1.81/1.54 % (3124)Termination phase: Saturation
% 1.81/1.54
% 1.81/1.54 % (3124)Memory used [KB]: 5628
% 1.81/1.54 % (3124)Time elapsed: 0.012 s
% 1.81/1.54 % (3124)Instructions burned: 19 (million)
% 1.81/1.54 % (3124)------------------------------
% 1.81/1.54 % (3124)------------------------------
% 1.81/1.55 % (3126)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/6Mi)
% 1.81/1.55 % (3126)Instruction limit reached!
% 1.81/1.55 % (3126)------------------------------
% 1.81/1.55 % (3126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.55 % (3126)Termination reason: Unknown
% 1.81/1.55 % (3126)Termination phase: Saturation
% 1.81/1.55
% 1.81/1.55 % (3126)Memory used [KB]: 5500
% 1.81/1.55 % (3126)Time elapsed: 0.006 s
% 1.81/1.55 % (3126)Instructions burned: 7 (million)
% 1.81/1.55 % (3126)------------------------------
% 1.81/1.55 % (3126)------------------------------
% 1.81/1.55 % (3127)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_3007 for (2999ds/902Mi)
% 1.81/1.56 % (3128)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_3007 for (2999ds/21Mi)
% 1.81/1.57 % (3129)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3007 for (2999ds/5Mi)
% 1.81/1.57 % (3105)Instruction limit reached!
% 1.81/1.57 % (3105)------------------------------
% 1.81/1.57 % (3105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.57 % (3105)Termination reason: Unknown
% 1.81/1.57 % (3105)Termination phase: Saturation
% 1.81/1.57
% 1.81/1.57 % (3105)Memory used [KB]: 6012
% 1.81/1.57 % (3105)Time elapsed: 0.103 s
% 1.81/1.57 % (3105)Instructions burned: 183 (million)
% 1.81/1.57 % (3105)------------------------------
% 1.81/1.57 % (3105)------------------------------
% 1.81/1.57 % (3129)Instruction limit reached!
% 1.81/1.57 % (3129)------------------------------
% 1.81/1.57 % (3129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.57 % (3129)Termination reason: Unknown
% 1.81/1.57 % (3129)Termination phase: Saturation
% 1.81/1.57
% 1.81/1.57 % (3129)Memory used [KB]: 5500
% 1.81/1.57 % (3129)Time elapsed: 0.005 s
% 1.81/1.57 % (3129)Instructions burned: 5 (million)
% 1.81/1.57 % (3129)------------------------------
% 1.81/1.57 % (3129)------------------------------
% 1.81/1.58 % (3128)Instruction limit reached!
% 1.81/1.58 % (3128)------------------------------
% 1.81/1.58 % (3128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.58 % (3128)Termination reason: Unknown
% 1.81/1.58 % (3128)Termination phase: Saturation
% 1.81/1.58
% 1.81/1.58 % (3128)Memory used [KB]: 5628
% 1.81/1.58 % (3128)Time elapsed: 0.014 s
% 1.81/1.58 % (3128)Instructions burned: 22 (million)
% 1.81/1.58 % (3128)------------------------------
% 1.81/1.58 % (3128)------------------------------
% 1.81/1.59 % (3131)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3007 for (2998ds/377Mi)
% 1.81/1.59 % (3130)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_3007 for (2998ds/6Mi)
% 1.81/1.59 % (3130)Instruction limit reached!
% 1.81/1.59 % (3130)------------------------------
% 1.81/1.59 % (3130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.59 % (3130)Termination reason: Unknown
% 1.81/1.59 % (3130)Termination phase: Saturation
% 1.81/1.59
% 1.81/1.59 % (3130)Memory used [KB]: 5500
% 1.81/1.59 % (3130)Time elapsed: 0.006 s
% 1.81/1.59 % (3130)Instructions burned: 7 (million)
% 1.81/1.59 % (3130)------------------------------
% 1.81/1.59 % (3130)------------------------------
% 1.81/1.59 % (3132)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_3007 for (2998ds/779Mi)
% 1.81/1.60 % (3110)Instruction limit reached!
% 1.81/1.60 % (3110)------------------------------
% 1.81/1.60 % (3110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.60 % (3110)Termination reason: Unknown
% 1.81/1.60 % (3110)Termination phase: Saturation
% 1.81/1.60
% 1.81/1.60 % (3110)Memory used [KB]: 5756
% 1.81/1.60 % (3110)Time elapsed: 0.139 s
% 1.81/1.60 % (3110)Instructions burned: 276 (million)
% 1.81/1.60 % (3110)------------------------------
% 1.81/1.60 % (3110)------------------------------
% 1.81/1.61 % (3133)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_3007 for (2998ds/19Mi)
% 1.81/1.62 % (3134)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3007 for (2998ds/879Mi)
% 1.81/1.63 % (3133)Instruction limit reached!
% 1.81/1.63 % (3133)------------------------------
% 1.81/1.63 % (3133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.63 % (3133)Termination reason: Unknown
% 1.81/1.63 % (3133)Termination phase: Saturation
% 1.81/1.63
% 1.81/1.63 % (3133)Memory used [KB]: 5628
% 1.81/1.63 % (3133)Time elapsed: 0.014 s
% 1.81/1.63 % (3133)Instructions burned: 20 (million)
% 1.81/1.63 % (3133)------------------------------
% 1.81/1.63 % (3133)------------------------------
% 1.81/1.63 % (3116)First to succeed.
% 1.81/1.64 % (3116)Refutation found. Thanks to Tanya!
% 1.81/1.64 % SZS status Theorem for DTF2THF_3007
% 1.81/1.64 % SZS output start Proof for DTF2THF_3007
% 1.81/1.64 thf(type_def_5, type, a: $tType).
% 1.81/1.64 thf(type_def_7, type, b: $tType).
% 1.81/1.64 thf(func_def_0, type, a: $tType).
% 1.81/1.64 thf(func_def_1, type, b: $tType).
% 1.81/1.64 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.81/1.64 thf(func_def_20, type, sK2: a > b > b > $o).
% 1.81/1.64 thf(func_def_21, type, sK3: a > a > $o).
% 1.81/1.64 thf(func_def_22, type, sK4: a > b).
% 1.81/1.64 thf(func_def_23, type, sK5: a > b).
% 1.81/1.64 thf(func_def_24, type, sK6: a > b).
% 1.81/1.64 thf(func_def_25, type, sK7: a > b).
% 1.81/1.64 thf(func_def_26, type, sK8: a).
% 1.81/1.64 thf(func_def_27, type, sK9: a).
% 1.81/1.64 thf(func_def_28, type, sK10: a > b).
% 1.81/1.64 thf(func_def_29, type, sK11: a > b).
% 1.81/1.64 thf(func_def_30, type, sK12: a).
% 1.81/1.64 thf(func_def_31, type, sK13: a).
% 1.81/1.64 thf(f1151,plain,(
% 1.81/1.64 $false),
% 1.81/1.64 inference(avatar_sat_refutation,[status(thm)],[f42,f820,f849,f1150])).
% 1.81/1.64 thf(f1150,plain,(
% 1.81/1.64 ~spl0_1 | ~spl0_4),
% 1.81/1.64 inference(avatar_contradiction_clause,[status(thm)],[f1149])).
% 1.81/1.64 thf(f1149,plain,(
% 1.81/1.64 $false | (~spl0_1 | ~spl0_4)),
% 1.81/1.64 inference(trivial_inequality_removal,[status(thm)],[f1148])).
% 1.81/1.64 thf(f1148,plain,(
% 1.81/1.64 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f1147])).
% 1.81/1.64 thf(f1147,plain,(
% 1.81/1.64 ($true = (~ $true)) | (~spl0_1 | ~spl0_4)),
% 1.81/1.64 inference(forward_demodulation,[status(thm)],[f1138,f1036])).
% 1.81/1.64 thf(f1036,plain,(
% 1.81/1.64 ($true = (sK2 @ sK12 @ (sK10 @ sK13) @ (sK11 @ sK12))) | ~spl0_1),
% 1.81/1.64 inference(superposition,[status(thm)],[f882,f1016])).
% 1.81/1.64 thf(f1016,plain,(
% 1.81/1.64 ( ! [X2 : b,X1 : b] : (((sK2 @ sK13 @ X1 @ X2) = (sK2 @ sK12 @ X1 @ X2))) ) | ~spl0_1),
% 1.81/1.64 inference(argument_congruence,[status(thm)],[f1013])).
% 1.81/1.64 thf(f1013,plain,(
% 1.81/1.64 ( ! [X1 : b] : (((sK2 @ sK13 @ X1) = (sK2 @ sK12 @ X1))) ) | ~spl0_1),
% 1.81/1.64 inference(argument_congruence,[status(thm)],[f1006])).
% 1.81/1.64 thf(f1006,plain,(
% 1.81/1.64 ((sK2 @ sK12) = (sK2 @ sK13)) | ~spl0_1),
% 1.81/1.64 inference(equality_proxy_clausification,[status(thm)],[f858])).
% 1.81/1.64 thf(f858,plain,(
% 1.81/1.64 ($true = ((sK2 @ sK13) = (sK2 @ sK12))) | ~spl0_1),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f855])).
% 1.81/1.64 thf(f855,plain,(
% 1.81/1.64 ($true = ($true => ((sK2 @ sK13) = (sK2 @ sK12)))) | ~spl0_1),
% 1.81/1.64 inference(superposition,[status(thm)],[f195,f836])).
% 1.81/1.64 thf(f836,plain,(
% 1.81/1.64 ($true = (sK3 @ sK12 @ sK13)) | ~spl0_1),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f834])).
% 1.81/1.64 thf(f834,plain,(
% 1.81/1.64 (((sK3 @ sK12 @ sK13) => (sK2 @ sK12 @ (sK11 @ sK12) @ (sK10 @ sK13))) = $false) | ~spl0_1),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f833])).
% 1.81/1.64 thf(f833,plain,(
% 1.81/1.64 ($false = ((^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK2 @ sK12 @ (sK11 @ sK12) @ (sK10 @ Y0)))) @ sK13)) | ~spl0_1),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f832])).
% 1.81/1.64 thf(f832,plain,(
% 1.81/1.64 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK2 @ sK12 @ (sK11 @ sK12) @ (sK10 @ Y0))))) = $false) | ~spl0_1),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f831])).
% 1.81/1.64 thf(f831,plain,(
% 1.81/1.64 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK11 @ Y0) @ (sK10 @ Y1)))))) @ sK12) = $false) | ~spl0_1),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f830])).
% 1.81/1.64 thf(f830,plain,(
% 1.81/1.64 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK11 @ Y0) @ (sK10 @ Y1))))))) = $false) | ~spl0_1),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f829])).
% 1.81/1.64 thf(f829,plain,(
% 1.81/1.64 (($true => (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK11 @ Y0) @ (sK10 @ Y1)))))))) = $false) | ~spl0_1),
% 1.81/1.64 inference(backward_demodulation,[status(thm)],[f826,f828])).
% 1.81/1.64 thf(f828,plain,(
% 1.81/1.64 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK10 @ Y0) @ (sK11 @ Y1)))))))) | ~spl0_1),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f826])).
% 1.81/1.64 thf(f826,plain,(
% 1.81/1.64 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK10 @ Y0) @ (sK11 @ Y1))))))) => (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK11 @ Y0) @ (sK10 @ Y1))))))))) | ~spl0_1),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f825])).
% 1.81/1.64 thf(f825,plain,(
% 1.81/1.64 (((^[Y0 : a > b]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK2 @ Y1 @ (sK10 @ Y1) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK2 @ Y1 @ (Y0 @ Y1) @ (sK10 @ Y2))))))))) @ sK11) = $false) | ~spl0_1),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f824])).
% 1.81/1.64 thf(f824,plain,(
% 1.81/1.64 ((!! @ (a > b) @ (^[Y0 : a > b]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK2 @ Y1 @ (sK10 @ Y1) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK2 @ Y1 @ (Y0 @ Y1) @ (sK10 @ Y2)))))))))) = $false) | ~spl0_1),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f823])).
% 1.81/1.64 thf(f823,plain,(
% 1.81/1.64 (((^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y1 @ Y2) @ (Y0 @ Y3))))))))))) @ sK10) = $false) | ~spl0_1),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f38])).
% 1.81/1.64 thf(f38,plain,(
% 1.81/1.64 ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y1 @ Y2) @ (Y0 @ Y3)))))))))))) = $false) | ~spl0_1),
% 1.81/1.64 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.81/1.64 thf(f37,definition,(
% 1.81/1.64 spl0_1 <=> ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y1 @ Y2) @ (Y0 @ Y3)))))))))))) = $false)),
% 1.81/1.64 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.81/1.64 thf(f195,plain,(
% 1.81/1.64 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X1 @ X2) => ((sK2 @ X2) = (sK2 @ X1))))) )),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f194])).
% 1.81/1.64 thf(f194,plain,(
% 1.81/1.64 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ X1 @ Y0) => ((sK2 @ Y0) = (sK2 @ X1)))) @ X2))) )),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f191])).
% 1.81/1.64 thf(f191,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) => ((sK2 @ Y0) = (sK2 @ X1))))))) )),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f190])).
% 1.81/1.64 thf(f190,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => ((sK2 @ Y1) = (sK2 @ Y0)))))) @ X1))) )),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f187])).
% 1.81/1.64 thf(f187,plain,(
% 1.81/1.64 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => ((sK2 @ Y1) = (sK2 @ Y0))))))))),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f186])).
% 1.81/1.64 thf(f186,plain,(
% 1.81/1.64 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => ((sK2 @ Y1) = (sK2 @ Y0))))))) & $true))),
% 1.81/1.64 inference(backward_demodulation,[status(thm)],[f32,f184])).
% 1.81/1.64 thf(f184,plain,(
% 1.81/1.64 ($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) => ((!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (((sK2 @ Y0 @ Y2 @ Y1) & (sK2 @ Y0 @ Y1 @ Y3)) => (sK2 @ Y0 @ Y2 @ Y3)))))))) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: ((sK2 @ Y0 @ Y2 @ Y1) => (sK2 @ Y0 @ Y1 @ Y2)))))))))))),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.81/1.64 thf(f32,plain,(
% 1.81/1.64 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => ((sK2 @ Y1) = (sK2 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) => ((!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (((sK2 @ Y0 @ Y2 @ Y1) & (sK2 @ Y0 @ Y1 @ Y3)) => (sK2 @ Y0 @ Y2 @ Y3)))))))) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: ((sK2 @ Y0 @ Y2 @ Y1) => (sK2 @ Y0 @ Y1 @ Y2))))))))))))),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.81/1.64 thf(f21,plain,(
% 1.81/1.64 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => ((sK2 @ Y1) = (sK2 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) => ((!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (((sK2 @ Y0 @ Y2 @ Y1) & (sK2 @ Y0 @ Y1 @ Y3)) => (sK2 @ Y0 @ Y2 @ Y3)))))))) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: ((sK2 @ Y0 @ Y2 @ Y1) => (sK2 @ Y0 @ Y1 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0))))))))),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.81/1.64 thf(f15,plain,(
% 1.81/1.64 ($true = ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => ((sK2 @ Y1) = (sK2 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) => ((!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (((sK2 @ Y0 @ Y2 @ Y1) & (sK2 @ Y0 @ Y1 @ Y3)) => (sK2 @ Y0 @ Y2 @ Y3)))))))) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: ((sK2 @ Y0 @ Y2 @ Y1) => (sK2 @ Y0 @ Y1 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y0) & (sK3 @ Y1 @ Y2)) => (sK3 @ Y1 @ Y0))))))))))),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.81/1.64 thf(f13,plain,(
% 1.81/1.64 ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => ((sK2 @ Y1) = (sK2 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) => ((!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (((sK2 @ Y0 @ Y2 @ Y1) & (sK2 @ Y0 @ Y1 @ Y3)) => (sK2 @ Y0 @ Y2 @ Y3)))))))) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: ((sK2 @ Y0 @ Y2 @ Y1) => (sK2 @ Y0 @ Y1 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y0) & (sK3 @ Y1 @ Y2)) => (sK3 @ Y1 @ Y0))))))))) => ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y1 @ Y2) @ (Y0 @ Y3)))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (sK2 @ Y4 @ (Y2 @ Y4) @ (Y1 @ Y3)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))))) = $false)),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.81/1.64 thf(f12,plain,(
% 1.81/1.64 ($false = ((^[Y0 : a > a > $o]: (((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => ((sK2 @ Y2) = (sK2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1 @ Y1) => ((!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (((sK2 @ Y1 @ Y3 @ Y2) & (sK2 @ Y1 @ Y2 @ Y4)) => (sK2 @ Y1 @ Y3 @ Y4)))))))) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: ((sK2 @ Y1 @ Y3 @ Y2) => (sK2 @ Y1 @ Y2 @ Y3))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => ((!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: ((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y1 @ Y3) @ (Y2 @ Y4))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))))))) & (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK2 @ Y4 @ (Y1 @ Y4) @ (Y3 @ Y5))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y5 @ Y4) => (sK2 @ Y5 @ (Y3 @ Y5) @ (Y2 @ Y4)))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK2 @ Y4 @ (Y1 @ Y4) @ (Y2 @ Y5))))))))))))))))) @ sK3))),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f11])).
% 1.81/1.64 thf(f11,plain,(
% 1.81/1.64 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => ((sK2 @ Y2) = (sK2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1 @ Y1) => ((!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (((sK2 @ Y1 @ Y3 @ Y2) & (sK2 @ Y1 @ Y2 @ Y4)) => (sK2 @ Y1 @ Y3 @ Y4)))))))) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: ((sK2 @ Y1 @ Y3 @ Y2) => (sK2 @ Y1 @ Y2 @ Y3))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => ((!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: ((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y1 @ Y3) @ (Y2 @ Y4))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))))))) & (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK2 @ Y4 @ (Y1 @ Y4) @ (Y3 @ Y5))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y5 @ Y4) => (sK2 @ Y5 @ (Y3 @ Y5) @ (Y2 @ Y4)))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK2 @ Y4 @ (Y1 @ Y4) @ (Y2 @ Y5)))))))))))))))))))),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.81/1.64 thf(f10,plain,(
% 1.81/1.64 ($false = ((^[Y0 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => ((Y0 @ Y3) = (Y0 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) => ((!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: (((Y0 @ Y2 @ Y4 @ Y3) & (Y0 @ Y2 @ Y3 @ Y5)) => (Y0 @ Y2 @ Y4 @ Y5)))))))) & (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: ((Y0 @ Y2 @ Y4 @ Y3) => (Y0 @ Y2 @ Y3 @ Y4))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => ((!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: ((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y2 @ Y4) @ (Y3 @ Y5))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y3 @ Y4) @ (Y2 @ Y5)))))))))))) & (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y4 @ Y6))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y6 @ Y5) => (Y0 @ Y6 @ (Y4 @ Y6) @ (Y3 @ Y5)))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y3 @ Y6))))))))))))))))))) @ sK2))),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f7])).
% 1.81/1.64 thf(f7,plain,(
% 1.81/1.64 ($false = (!! @ (a > b > b > $o) @ (^[Y0 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => ((Y0 @ Y3) = (Y0 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) => ((!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: (((Y0 @ Y2 @ Y4 @ Y3) & (Y0 @ Y2 @ Y3 @ Y5)) => (Y0 @ Y2 @ Y4 @ Y5)))))))) & (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: ((Y0 @ Y2 @ Y4 @ Y3) => (Y0 @ Y2 @ Y3 @ Y4))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => ((!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: ((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y2 @ Y4) @ (Y3 @ Y5))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y3 @ Y4) @ (Y2 @ Y5)))))))))))) & (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y4 @ Y6))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y6 @ Y5) => (Y0 @ Y6 @ (Y4 @ Y6) @ (Y3 @ Y5)))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y3 @ Y6)))))))))))))))))))))),
% 1.81/1.64 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.81/1.64 thf(f6,plain,(
% 1.81/1.64 ($true = (~ (!! @ (a > b > b > $o) @ (^[Y0 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => ((Y0 @ Y3) = (Y0 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) => ((!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: (((Y0 @ Y2 @ Y4 @ Y3) & (Y0 @ Y2 @ Y3 @ Y5)) => (Y0 @ Y2 @ Y4 @ Y5)))))))) & (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: ((Y0 @ Y2 @ Y4 @ Y3) => (Y0 @ Y2 @ Y3 @ Y4))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => ((!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: ((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y2 @ Y4) @ (Y3 @ Y5))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y3 @ Y4) @ (Y2 @ Y5)))))))))))) & (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y4 @ Y6))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y6 @ Y5) => (Y0 @ Y6 @ (Y4 @ Y6) @ (Y3 @ Y5)))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y3 @ Y6))))))))))))))))))))))),
% 1.81/1.64 inference(cnf_transformation,[status(thm)],[f5])).
% 1.81/1.64 thf(f5,plain,(
% 1.81/1.64 ($true = (~ (!! @ (a > b > b > $o) @ (^[Y0 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => ((Y0 @ Y3) = (Y0 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) => ((!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: (((Y0 @ Y2 @ Y4 @ Y3) & (Y0 @ Y2 @ Y3 @ Y5)) => (Y0 @ Y2 @ Y4 @ Y5)))))))) & (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: ((Y0 @ Y2 @ Y4 @ Y3) => (Y0 @ Y2 @ Y3 @ Y4))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => ((!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: ((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y2 @ Y4) @ (Y3 @ Y5))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y3 @ Y4) @ (Y2 @ Y5)))))))))))) & (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y4 @ Y6))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y6 @ Y5) => (Y0 @ Y6 @ (Y4 @ Y6) @ (Y3 @ Y5)))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y3 @ Y6))))))))))))))))))))))),
% 1.81/1.64 inference(fool_elimination,[status(thm)],[f4])).
% 1.81/1.64 thf(f4,plain,(
% 1.81/1.64 ~! [X0 : a > a > $o,X1 : a > b > b > $o] : ((! [X2 : a,X3 : a,X4 : a] : (((X0 @ X3 @ X2) & (X0 @ X2 @ X4)) => (X0 @ X3 @ X4)) & ! [X5 : a,X6 : a] : ((X0 @ X6 @ X5) => (X0 @ X5 @ X6)) & ! [X7 : a] : ((X0 @ X7 @ X7) => (! [X8 : b,X9 : b] : ((X1 @ X7 @ X8 @ X9) => (X1 @ X7 @ X9 @ X8)) & ! [X10 : b,X11 : b,X12 : b] : (((X1 @ X7 @ X12 @ X10) & (X1 @ X7 @ X11 @ X12)) => (X1 @ X7 @ X11 @ X10)))) & ! [X13 : a,X14 : a] : ((X0 @ X14 @ X13) => ((X1 @ X13) = (X1 @ X14)))) => (! [X15 : a > b,X16 : a > b,X17 : a > b] : ((! [X18 : a,X19 : a] : ((X0 @ X18 @ X19) => (X1 @ X18 @ (X15 @ X18) @ (X16 @ X19))) & ! [X20 : a,X21 : a] : ((X0 @ X21 @ X20) => (X1 @ X21 @ (X17 @ X21) @ (X15 @ X20)))) => ! [X22 : a,X23 : a] : ((X0 @ X23 @ X22) => (X1 @ X23 @ (X17 @ X23) @ (X16 @ X22)))) & ! [X24 : a > b,X25 : a > b] : (! [X26 : a,X27 : a] : ((X0 @ X27 @ X26) => (X1 @ X27 @ (X25 @ X27) @ (X24 @ X26))) => ! [X28 : a,X29 : a] : ((X0 @ X29 @ X28) => (X1 @ X29 @ (X24 @ X29) @ (X25 @ X28))))))),
% 1.81/1.64 inference(rectify,[status(thm)],[f2])).
% 1.81/1.64 thf(f2,negated_conjecture,(
% 1.81/1.64 ~! [X0 : a > a > $o,X1 : a > b > b > $o] : ((! [X3 : a,X2 : a,X4 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4)) & ! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)) & ! [X2 : a] : ((X0 @ X2 @ X2) => (! [X5 : b,X3 : b] : ((X1 @ X2 @ X5 @ X3) => (X1 @ X2 @ X3 @ X5)) & ! [X4 : b,X5 : b,X3 : b] : (((X1 @ X2 @ X3 @ X4) & (X1 @ X2 @ X5 @ X3)) => (X1 @ X2 @ X5 @ X4)))) & ! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => ((X1 @ X2) = (X1 @ X3)))) => (! [X3 : a > b,X4 : a > b,X2 : a > b] : ((! [X5 : a,X6 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X3 @ X5) @ (X4 @ X6))) & ! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X2 @ X5) @ (X3 @ X6)))) => ! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X2 @ X5) @ (X4 @ X6)))) & ! [X3 : a > b,X2 : a > b] : (! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X2 @ X5) @ (X3 @ X6))) => ! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X3 @ X5) @ (X2 @ X6))))))),
% 1.81/1.64 inference(negated_conjecture,[status(cth)],[f1])).
% 1.81/1.64 thf(f1,conjecture,(
% 1.81/1.64 ! [X0 : a > a > $o,X1 : a > b > b > $o] : ((! [X3 : a,X2 : a,X4 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4)) & ! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)) & ! [X2 : a] : ((X0 @ X2 @ X2) => (! [X5 : b,X3 : b] : ((X1 @ X2 @ X5 @ X3) => (X1 @ X2 @ X3 @ X5)) & ! [X4 : b,X5 : b,X3 : b] : (((X1 @ X2 @ X3 @ X4) & (X1 @ X2 @ X5 @ X3)) => (X1 @ X2 @ X5 @ X4)))) & ! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => ((X1 @ X2) = (X1 @ X3)))) => (! [X3 : a > b,X4 : a > b,X2 : a > b] : ((! [X5 : a,X6 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X3 @ X5) @ (X4 @ X6))) & ! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X2 @ X5) @ (X3 @ X6)))) => ! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X2 @ X5) @ (X4 @ X6)))) & ! [X3 : a > b,X2 : a > b] : (! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X2 @ X5) @ (X3 @ X6))) => ! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X3 @ X5) @ (X2 @ X6))))))),
% 1.81/1.64 file('/export/starexec/sandbox/tmp/tmp.kat0iVf5Pk/DTF2THF_3007.p',cTHM507_pme)).
% 1.81/1.64 thf(f882,plain,(
% 1.81/1.64 ($true = (sK2 @ sK13 @ (sK10 @ sK13) @ (sK11 @ sK12))) | ~spl0_1),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f880])).
% 1.81/1.64 thf(f880,plain,(
% 1.81/1.64 ($true = ($true => (sK2 @ sK13 @ (sK10 @ sK13) @ (sK11 @ sK12)))) | ~spl0_1),
% 1.81/1.64 inference(superposition,[status(thm)],[f877,f856])).
% 1.81/1.64 thf(f856,plain,(
% 1.81/1.64 ($true = (sK3 @ sK13 @ sK12)) | ~spl0_1),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f853])).
% 1.81/1.64 thf(f853,plain,(
% 1.81/1.64 ($true = ($true => (sK3 @ sK13 @ sK12))) | ~spl0_1),
% 1.81/1.64 inference(superposition,[status(thm)],[f50,f836])).
% 1.81/1.64 thf(f50,plain,(
% 1.81/1.64 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X1 @ X2) => (sK3 @ X2 @ X1)))) )),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.81/1.64 thf(f49,plain,(
% 1.81/1.64 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK3 @ Y0 @ X1))) @ X2))) )),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f46])).
% 1.81/1.64 thf(f46,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK3 @ Y0 @ X1)))))) )),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.81/1.64 thf(f45,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0))))) @ X1))) )),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f34])).
% 1.81/1.64 thf(f34,plain,(
% 1.81/1.64 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0)))))))),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f33])).
% 1.81/1.64 thf(f33,plain,(
% 1.81/1.64 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0))))))))),
% 1.81/1.64 inference(backward_demodulation,[status(thm)],[f21,f32])).
% 1.81/1.64 thf(f877,plain,(
% 1.81/1.64 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X1 @ X2) => (sK2 @ X1 @ (sK10 @ X1) @ (sK11 @ X2))))) ) | ~spl0_1),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f876])).
% 1.81/1.64 thf(f876,plain,(
% 1.81/1.64 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK2 @ X1 @ (sK10 @ X1) @ (sK11 @ Y0)))) @ X2))) ) | ~spl0_1),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f863])).
% 1.81/1.64 thf(f863,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK2 @ X1 @ (sK10 @ X1) @ (sK11 @ Y0))))))) ) | ~spl0_1),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f862])).
% 1.81/1.64 thf(f862,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK10 @ Y0) @ (sK11 @ Y1)))))) @ X1))) ) | ~spl0_1),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f828])).
% 1.81/1.64 thf(f1138,plain,(
% 1.81/1.64 ($true = (~ (sK2 @ sK12 @ (sK10 @ sK13) @ (sK11 @ sK12)))) | (~spl0_1 | ~spl0_4)),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f1124])).
% 1.81/1.64 thf(f1124,plain,(
% 1.81/1.64 ($true = ((sK2 @ sK12 @ (sK10 @ sK13) @ (sK11 @ sK12)) => $false)) | (~spl0_1 | ~spl0_4)),
% 1.81/1.64 inference(superposition,[status(thm)],[f1089,f844])).
% 1.81/1.64 thf(f844,plain,(
% 1.81/1.64 ($false = (sK2 @ sK12 @ (sK11 @ sK12) @ (sK10 @ sK13))) | ~spl0_4),
% 1.81/1.64 inference(avatar_component_clause,[status(thm)],[f843])).
% 1.81/1.64 thf(f843,definition,(
% 1.81/1.64 spl0_4 <=> ($false = (sK2 @ sK12 @ (sK11 @ sK12) @ (sK10 @ sK13)))),
% 1.81/1.64 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.81/1.64 thf(f1089,plain,(
% 1.81/1.64 ( ! [X2 : b,X1 : b] : (($true = ((sK2 @ sK12 @ X2 @ X1) => (sK2 @ sK12 @ X1 @ X2)))) ) | ~spl0_1),
% 1.81/1.64 inference(forward_demodulation,[status(thm)],[f1088,f1016])).
% 1.81/1.64 thf(f1088,plain,(
% 1.81/1.64 ( ! [X2 : b,X1 : b] : (($true = ((sK2 @ sK12 @ X2 @ X1) => (sK2 @ sK13 @ X1 @ X2)))) ) | ~spl0_1),
% 1.81/1.64 inference(forward_demodulation,[status(thm)],[f1087,f1016])).
% 1.81/1.64 thf(f1087,plain,(
% 1.81/1.64 ( ! [X2 : b,X1 : b] : (($true = ((sK2 @ sK13 @ X2 @ X1) => (sK2 @ sK13 @ X1 @ X2)))) ) | ~spl0_1),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f1086])).
% 1.81/1.64 thf(f1086,plain,(
% 1.81/1.64 ( ! [X2 : b,X1 : b] : (($true = ((^[Y0 : b]: ((sK2 @ sK13 @ Y0 @ X1) => (sK2 @ sK13 @ X1 @ Y0))) @ X2))) ) | ~spl0_1),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f1078])).
% 1.81/1.64 thf(f1078,plain,(
% 1.81/1.64 ( ! [X1 : b] : (($true = (!! @ b @ (^[Y0 : b]: ((sK2 @ sK13 @ Y0 @ X1) => (sK2 @ sK13 @ X1 @ Y0)))))) ) | ~spl0_1),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f1075])).
% 1.81/1.64 thf(f1075,plain,(
% 1.81/1.64 ( ! [X1 : b] : (($true = ((^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK2 @ sK13 @ Y1 @ Y0) => (sK2 @ sK13 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_1),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f1050])).
% 1.81/1.64 thf(f1050,plain,(
% 1.81/1.64 ($true = (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK2 @ sK13 @ Y1 @ Y0) => (sK2 @ sK13 @ Y0 @ Y1))))))) | ~spl0_1),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f911])).
% 1.81/1.64 thf(f911,plain,(
% 1.81/1.64 ($true = ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK2 @ sK13 @ Y1 @ Y0) & (sK2 @ sK13 @ Y0 @ Y2)) => (sK2 @ sK13 @ Y1 @ Y2)))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK2 @ sK13 @ Y1 @ Y0) => (sK2 @ sK13 @ Y0 @ Y1)))))))) | ~spl0_1),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f897])).
% 1.81/1.64 thf(f897,plain,(
% 1.81/1.64 ($true = ($true => ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK2 @ sK13 @ Y1 @ Y0) & (sK2 @ sK13 @ Y0 @ Y2)) => (sK2 @ sK13 @ Y1 @ Y2)))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK2 @ sK13 @ Y1 @ Y0) => (sK2 @ sK13 @ Y0 @ Y1))))))))) | ~spl0_1),
% 1.81/1.64 inference(superposition,[status(thm)],[f253,f894])).
% 1.81/1.64 thf(f894,plain,(
% 1.81/1.64 ($true = (sK3 @ sK13 @ sK13)) | ~spl0_1),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f890])).
% 1.81/1.64 thf(f890,plain,(
% 1.81/1.64 ($true = ($true => (sK3 @ sK13 @ sK13))) | ~spl0_1),
% 1.81/1.64 inference(superposition,[status(thm)],[f857,f856])).
% 1.81/1.64 thf(f857,plain,(
% 1.81/1.64 ( ! [X0 : a] : (($true = ((sK3 @ X0 @ sK12) => (sK3 @ X0 @ sK13)))) ) | ~spl0_1),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f850])).
% 1.81/1.64 thf(f850,plain,(
% 1.81/1.64 ( ! [X0 : a] : (($true = (($true & (sK3 @ X0 @ sK12)) => (sK3 @ X0 @ sK13)))) ) | ~spl0_1),
% 1.81/1.64 inference(superposition,[status(thm)],[f29,f836])).
% 1.81/1.64 thf(f29,plain,(
% 1.81/1.64 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK3 @ X3 @ X1) & (sK3 @ X2 @ X3)) => (sK3 @ X2 @ X1)))) )),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.81/1.64 thf(f28,plain,(
% 1.81/1.64 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK3 @ Y0 @ X1) & (sK3 @ X2 @ Y0)) => (sK3 @ X2 @ X1))) @ X3))) )),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f27])).
% 1.81/1.64 thf(f27,plain,(
% 1.81/1.64 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK3 @ Y0 @ X1) & (sK3 @ X2 @ Y0)) => (sK3 @ X2 @ X1)))))) )),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.81/1.64 thf(f26,plain,(
% 1.81/1.64 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ X1) & (sK3 @ Y0 @ Y1)) => (sK3 @ Y0 @ X1))))) @ X2))) )),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f25])).
% 1.81/1.64 thf(f25,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ X1) & (sK3 @ Y0 @ Y1)) => (sK3 @ Y0 @ X1)))))))) )),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.81/1.64 thf(f24,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y0) & (sK3 @ Y1 @ Y2)) => (sK3 @ Y1 @ Y0))))))) @ X1))) )),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f23])).
% 1.81/1.64 thf(f23,plain,(
% 1.81/1.64 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y0) & (sK3 @ Y1 @ Y2)) => (sK3 @ Y1 @ Y0)))))))))),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f22])).
% 1.81/1.64 thf(f22,plain,(
% 1.81/1.64 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y0) & (sK3 @ Y1 @ Y2)) => (sK3 @ Y1 @ Y0))))))))))),
% 1.81/1.64 inference(backward_demodulation,[status(thm)],[f15,f21])).
% 1.81/1.64 thf(f253,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = ((sK3 @ X1 @ X1) => ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK2 @ X1 @ Y1 @ Y0) & (sK2 @ X1 @ Y0 @ Y2)) => (sK2 @ X1 @ Y1 @ Y2)))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK2 @ X1 @ Y1 @ Y0) => (sK2 @ X1 @ Y0 @ Y1)))))))))) )),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f252])).
% 1.81/1.64 thf(f252,plain,(
% 1.81/1.64 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ Y0 @ Y0) => ((!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (((sK2 @ Y0 @ Y2 @ Y1) & (sK2 @ Y0 @ Y1 @ Y3)) => (sK2 @ Y0 @ Y2 @ Y3)))))))) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: ((sK2 @ Y0 @ Y2 @ Y1) => (sK2 @ Y0 @ Y1 @ Y2))))))))) @ X1))) )),
% 1.81/1.64 inference(pi_clausification,[status(thm)],[f184])).
% 1.81/1.64 thf(f849,plain,(
% 1.81/1.64 spl0_4 | ~spl0_1),
% 1.81/1.64 inference(avatar_split_clause,[status(thm)],[f848,f37,f843])).
% 1.81/1.64 thf(f848,plain,(
% 1.81/1.64 ($false = (sK2 @ sK12 @ (sK11 @ sK12) @ (sK10 @ sK13))) | ~spl0_1),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f847])).
% 1.81/1.64 thf(f847,plain,(
% 1.81/1.64 ($false = ($true => (sK2 @ sK12 @ (sK11 @ sK12) @ (sK10 @ sK13)))) | ~spl0_1),
% 1.81/1.64 inference(backward_demodulation,[status(thm)],[f834,f836])).
% 1.81/1.64 thf(f820,plain,(
% 1.81/1.64 ~spl0_2),
% 1.81/1.64 inference(avatar_contradiction_clause,[status(thm)],[f819])).
% 1.81/1.64 thf(f819,plain,(
% 1.81/1.64 $false | ~spl0_2),
% 1.81/1.64 inference(trivial_inequality_removal,[status(thm)],[f818])).
% 1.81/1.64 thf(f818,plain,(
% 1.81/1.64 ($true = $false) | ~spl0_2),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f817])).
% 1.81/1.64 thf(f817,plain,(
% 1.81/1.64 ($true = (~ $true)) | ~spl0_2),
% 1.81/1.64 inference(forward_demodulation,[status(thm)],[f808,f180])).
% 1.81/1.64 thf(f180,plain,(
% 1.81/1.64 ($true = (sK2 @ sK8 @ (sK6 @ sK8) @ (sK5 @ sK9))) | ~spl0_2),
% 1.81/1.64 inference(boolean_simplification,[status(thm)],[f178])).
% 1.81/1.64 thf(f178,plain,(
% 1.81/1.64 ($true = ($true => (sK2 @ sK8 @ (sK6 @ sK8) @ (sK5 @ sK9)))) | ~spl0_2),
% 1.81/1.64 inference(superposition,[status(thm)],[f172,f78])).
% 1.81/1.64 thf(f78,plain,(
% 1.81/1.64 ($true = (sK3 @ sK8 @ sK9)) | ~spl0_2),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.81/1.64 thf(f72,plain,(
% 1.81/1.64 (((sK3 @ sK8 @ sK9) => (sK2 @ sK8 @ (sK4 @ sK8) @ (sK5 @ sK9))) = $false) | ~spl0_2),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.81/1.64 thf(f71,plain,(
% 1.81/1.64 (((^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK2 @ sK8 @ (sK4 @ sK8) @ (sK5 @ Y0)))) @ sK9) = $false) | ~spl0_2),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f67])).
% 1.81/1.64 thf(f67,plain,(
% 1.81/1.64 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK2 @ sK8 @ (sK4 @ sK8) @ (sK5 @ Y0)))))) | ~spl0_2),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.81/1.64 thf(f66,plain,(
% 1.81/1.64 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK4 @ Y0) @ (sK5 @ Y1)))))) @ sK8) = $false) | ~spl0_2),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f56])).
% 1.81/1.64 thf(f56,plain,(
% 1.81/1.64 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK4 @ Y0) @ (sK5 @ Y1))))))) = $false) | ~spl0_2),
% 1.81/1.64 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.81/1.64 thf(f55,plain,(
% 1.81/1.64 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK4 @ Y0) @ (sK6 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK2 @ Y1 @ (sK6 @ Y1) @ (sK5 @ Y0)))))))) => (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK4 @ Y0) @ (sK5 @ Y1))))))))) | ~spl0_2),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.81/1.64 thf(f54,plain,(
% 1.81/1.64 ($false = ((^[Y0 : a > b]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK2 @ Y1 @ (sK4 @ Y1) @ (Y0 @ Y2))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK2 @ Y2 @ (Y0 @ Y2) @ (sK5 @ Y1)))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK2 @ Y1 @ (sK4 @ Y1) @ (sK5 @ Y2))))))))) @ sK6)) | ~spl0_2),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f52])).
% 1.81/1.64 thf(f52,plain,(
% 1.81/1.64 ((!! @ (a > b) @ (^[Y0 : a > b]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK2 @ Y1 @ (sK4 @ Y1) @ (Y0 @ Y2))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK2 @ Y2 @ (Y0 @ Y2) @ (sK5 @ Y1)))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK2 @ Y1 @ (sK4 @ Y1) @ (sK5 @ Y2)))))))))) = $false) | ~spl0_2),
% 1.81/1.64 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.81/1.64 thf(f51,plain,(
% 1.81/1.64 (((^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (sK4 @ Y2) @ (Y1 @ Y3))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y3 @ Y2) => (sK2 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2)))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (sK4 @ Y2) @ (Y0 @ Y3))))))))))) @ sK5) = $false) | ~spl0_2),
% 1.81/1.64 inference(sigma_clausification,[status(thm)],[f48])).
% 1.81/1.64 thf(f48,plain,(
% 1.81/1.64 ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (sK4 @ Y2) @ (Y1 @ Y3))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y3 @ Y2) => (sK2 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2)))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (sK4 @ Y2) @ (Y0 @ Y3)))))))))))) = $false) | ~spl0_2),
% 1.81/1.65 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.81/1.65 thf(f47,plain,(
% 1.81/1.65 (((^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (sK2 @ Y4 @ (Y2 @ Y4) @ (Y1 @ Y3)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4))))))))))))) @ sK4) = $false) | ~spl0_2),
% 1.81/1.65 inference(sigma_clausification,[status(thm)],[f41])).
% 1.81/1.65 thf(f41,plain,(
% 1.81/1.65 ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (sK2 @ Y4 @ (Y2 @ Y4) @ (Y1 @ Y3)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4))))))))))))))) | ~spl0_2),
% 1.81/1.65 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.81/1.65 thf(f40,definition,(
% 1.81/1.65 spl0_2 <=> ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (sK2 @ Y4 @ (Y2 @ Y4) @ (Y1 @ Y3)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))))),
% 1.81/1.65 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.81/1.65 thf(f172,plain,(
% 1.81/1.65 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X2 @ X1) => (sK2 @ X2 @ (sK6 @ X2) @ (sK5 @ X1))))) ) | ~spl0_2),
% 1.81/1.65 inference(beta_eta_normalization,[status(thm)],[f171])).
% 1.81/1.65 thf(f171,plain,(
% 1.81/1.65 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ Y0 @ X1) => (sK2 @ Y0 @ (sK6 @ Y0) @ (sK5 @ X1)))) @ X2))) ) | ~spl0_2),
% 1.81/1.65 inference(pi_clausification,[status(thm)],[f168])).
% 1.81/1.65 thf(f168,plain,(
% 1.81/1.65 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ X1) => (sK2 @ Y0 @ (sK6 @ Y0) @ (sK5 @ X1))))))) ) | ~spl0_2),
% 1.81/1.65 inference(beta_eta_normalization,[status(thm)],[f167])).
% 1.81/1.65 thf(f167,plain,(
% 1.81/1.65 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK2 @ Y1 @ (sK6 @ Y1) @ (sK5 @ Y0)))))) @ X1))) ) | ~spl0_2),
% 1.81/1.65 inference(pi_clausification,[status(thm)],[f125])).
% 1.81/1.65 thf(f125,plain,(
% 1.81/1.65 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK2 @ Y1 @ (sK6 @ Y1) @ (sK5 @ Y0)))))))) | ~spl0_2),
% 1.81/1.65 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.81/1.65 thf(f57,plain,(
% 1.81/1.65 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK4 @ Y0) @ (sK6 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK2 @ Y1 @ (sK6 @ Y1) @ (sK5 @ Y0))))))))) | ~spl0_2),
% 1.81/1.65 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.81/1.65 thf(f808,plain,(
% 1.81/1.65 ((~ (sK2 @ sK8 @ (sK6 @ sK8) @ (sK5 @ sK9))) = $true) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f798])).
% 1.81/1.65 thf(f798,plain,(
% 1.81/1.65 ($true = ((sK2 @ sK8 @ (sK6 @ sK8) @ (sK5 @ sK9)) => $false)) | ~spl0_2),
% 1.81/1.65 inference(superposition,[status(thm)],[f546,f80])).
% 1.81/1.65 thf(f80,plain,(
% 1.81/1.65 ((sK2 @ sK8 @ (sK4 @ sK8) @ (sK5 @ sK9)) = $false) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f79])).
% 1.81/1.65 thf(f79,plain,(
% 1.81/1.65 (($true => (sK2 @ sK8 @ (sK4 @ sK8) @ (sK5 @ sK9))) = $false) | ~spl0_2),
% 1.81/1.65 inference(backward_demodulation,[status(thm)],[f72,f78])).
% 1.81/1.65 thf(f546,plain,(
% 1.81/1.65 ( ! [X0 : b] : (($true = ((sK2 @ sK8 @ (sK6 @ sK8) @ X0) => (sK2 @ sK8 @ (sK4 @ sK8) @ X0)))) ) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f536])).
% 1.81/1.65 thf(f536,plain,(
% 1.81/1.65 ( ! [X0 : b] : (($true = (($true & (sK2 @ sK8 @ (sK6 @ sK8) @ X0)) => (sK2 @ sK8 @ (sK4 @ sK8) @ X0)))) ) | ~spl0_2),
% 1.81/1.65 inference(superposition,[status(thm)],[f477,f163])).
% 1.81/1.65 thf(f163,plain,(
% 1.81/1.65 ($true = (sK2 @ sK8 @ (sK4 @ sK8) @ (sK6 @ sK8))) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f160])).
% 1.81/1.65 thf(f160,plain,(
% 1.81/1.65 ($true = ($true => (sK2 @ sK8 @ (sK4 @ sK8) @ (sK6 @ sK8)))) | ~spl0_2),
% 1.81/1.65 inference(superposition,[status(thm)],[f139,f136])).
% 1.81/1.65 thf(f136,plain,(
% 1.81/1.65 ($true = (sK3 @ sK8 @ sK8)) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f135])).
% 1.81/1.65 thf(f135,plain,(
% 1.81/1.65 ($true = ($true => (sK3 @ sK8 @ sK8))) | ~spl0_2),
% 1.81/1.65 inference(superposition,[status(thm)],[f89,f91])).
% 1.81/1.65 thf(f91,plain,(
% 1.81/1.65 ($true = (sK3 @ sK9 @ sK8)) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f83])).
% 1.81/1.65 thf(f83,plain,(
% 1.81/1.65 ($true = ($true => (sK3 @ sK9 @ sK8))) | ~spl0_2),
% 1.81/1.65 inference(superposition,[status(thm)],[f50,f78])).
% 1.81/1.65 thf(f89,plain,(
% 1.81/1.65 ( ! [X0 : a] : (($true = ((sK3 @ sK9 @ X0) => (sK3 @ sK8 @ X0)))) ) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f86])).
% 1.81/1.65 thf(f86,plain,(
% 1.81/1.65 ( ! [X0 : a] : (($true = (((sK3 @ sK9 @ X0) & $true) => (sK3 @ sK8 @ X0)))) ) | ~spl0_2),
% 1.81/1.65 inference(superposition,[status(thm)],[f29,f78])).
% 1.81/1.65 thf(f139,plain,(
% 1.81/1.65 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X1 @ X2) => (sK2 @ X1 @ (sK4 @ X1) @ (sK6 @ X2))))) ) | ~spl0_2),
% 1.81/1.65 inference(beta_eta_normalization,[status(thm)],[f138])).
% 1.81/1.65 thf(f138,plain,(
% 1.81/1.65 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK2 @ X1 @ (sK4 @ X1) @ (sK6 @ Y0)))) @ X2))) ) | ~spl0_2),
% 1.81/1.65 inference(pi_clausification,[status(thm)],[f132])).
% 1.81/1.65 thf(f132,plain,(
% 1.81/1.65 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK2 @ X1 @ (sK4 @ X1) @ (sK6 @ Y0))))))) ) | ~spl0_2),
% 1.81/1.65 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.81/1.65 thf(f131,plain,(
% 1.81/1.65 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK4 @ Y0) @ (sK6 @ Y1)))))) @ X1))) ) | ~spl0_2),
% 1.81/1.65 inference(pi_clausification,[status(thm)],[f128])).
% 1.81/1.65 thf(f128,plain,(
% 1.81/1.65 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK4 @ Y0) @ (sK6 @ Y1)))))))) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f127])).
% 1.81/1.65 thf(f127,plain,(
% 1.81/1.65 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK2 @ Y0 @ (sK4 @ Y0) @ (sK6 @ Y1))))))) & $true)) | ~spl0_2),
% 1.81/1.65 inference(backward_demodulation,[status(thm)],[f57,f125])).
% 1.81/1.65 thf(f477,plain,(
% 1.81/1.65 ( ! [X2 : b,X3 : b,X1 : b] : (($true = (((sK2 @ sK8 @ X2 @ X1) & (sK2 @ sK8 @ X1 @ X3)) => (sK2 @ sK8 @ X2 @ X3)))) ) | ~spl0_2),
% 1.81/1.65 inference(beta_eta_normalization,[status(thm)],[f476])).
% 1.81/1.65 thf(f476,plain,(
% 1.81/1.65 ( ! [X2 : b,X3 : b,X1 : b] : (($true = ((^[Y0 : b]: (((sK2 @ sK8 @ X2 @ X1) & (sK2 @ sK8 @ X1 @ Y0)) => (sK2 @ sK8 @ X2 @ Y0))) @ X3))) ) | ~spl0_2),
% 1.81/1.65 inference(pi_clausification,[status(thm)],[f471])).
% 1.81/1.65 thf(f471,plain,(
% 1.81/1.65 ( ! [X2 : b,X1 : b] : (($true = (!! @ b @ (^[Y0 : b]: (((sK2 @ sK8 @ X2 @ X1) & (sK2 @ sK8 @ X1 @ Y0)) => (sK2 @ sK8 @ X2 @ Y0)))))) ) | ~spl0_2),
% 1.81/1.65 inference(beta_eta_normalization,[status(thm)],[f470])).
% 1.81/1.65 thf(f470,plain,(
% 1.81/1.65 ( ! [X2 : b,X1 : b] : (($true = ((^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (((sK2 @ sK8 @ Y0 @ X1) & (sK2 @ sK8 @ X1 @ Y1)) => (sK2 @ sK8 @ Y0 @ Y1))))) @ X2))) ) | ~spl0_2),
% 1.81/1.65 inference(pi_clausification,[status(thm)],[f462])).
% 1.81/1.65 thf(f462,plain,(
% 1.81/1.65 ( ! [X1 : b] : (($true = (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (((sK2 @ sK8 @ Y0 @ X1) & (sK2 @ sK8 @ X1 @ Y1)) => (sK2 @ sK8 @ Y0 @ Y1)))))))) ) | ~spl0_2),
% 1.81/1.65 inference(beta_eta_normalization,[status(thm)],[f460])).
% 1.81/1.65 thf(f460,plain,(
% 1.81/1.65 ( ! [X1 : b] : (($true = ((^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK2 @ sK8 @ Y1 @ Y0) & (sK2 @ sK8 @ Y0 @ Y2)) => (sK2 @ sK8 @ Y1 @ Y2))))))) @ X1))) ) | ~spl0_2),
% 1.81/1.65 inference(pi_clausification,[status(thm)],[f455])).
% 1.81/1.65 thf(f455,plain,(
% 1.81/1.65 ($true = (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK2 @ sK8 @ Y1 @ Y0) & (sK2 @ sK8 @ Y0 @ Y2)) => (sK2 @ sK8 @ Y1 @ Y2))))))))) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f454])).
% 1.81/1.65 thf(f454,plain,(
% 1.81/1.65 ($true = ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK2 @ sK8 @ Y1 @ Y0) & (sK2 @ sK8 @ Y0 @ Y2)) => (sK2 @ sK8 @ Y1 @ Y2)))))))) & $true)) | ~spl0_2),
% 1.81/1.65 inference(backward_demodulation,[status(thm)],[f260,f450])).
% 1.81/1.65 thf(f450,plain,(
% 1.81/1.65 ($true = (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK2 @ sK8 @ Y1 @ Y0) => (sK2 @ sK8 @ Y0 @ Y1))))))) | ~spl0_2),
% 1.81/1.65 inference(binary_proxy_clausification,[status(thm)],[f260])).
% 1.81/1.65 thf(f260,plain,(
% 1.81/1.65 ($true = ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK2 @ sK8 @ Y1 @ Y0) & (sK2 @ sK8 @ Y0 @ Y2)) => (sK2 @ sK8 @ Y1 @ Y2)))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK2 @ sK8 @ Y1 @ Y0) => (sK2 @ sK8 @ Y0 @ Y1)))))))) | ~spl0_2),
% 1.81/1.65 inference(boolean_simplification,[status(thm)],[f257])).
% 1.81/1.65 thf(f257,plain,(
% 1.81/1.65 ($true = ($true => ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK2 @ sK8 @ Y1 @ Y0) & (sK2 @ sK8 @ Y0 @ Y2)) => (sK2 @ sK8 @ Y1 @ Y2)))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK2 @ sK8 @ Y1 @ Y0) => (sK2 @ sK8 @ Y0 @ Y1))))))))) | ~spl0_2),
% 1.81/1.65 inference(superposition,[status(thm)],[f253,f136])).
% 1.81/1.65 thf(f42,plain,(
% 1.81/1.65 spl0_1 | spl0_2),
% 1.81/1.65 inference(avatar_split_clause,[status(thm)],[f35,f40,f37])).
% 1.81/1.65 thf(f35,plain,(
% 1.81/1.65 ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (sK2 @ Y4 @ (Y2 @ Y4) @ (Y1 @ Y3)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4))))))))))))))) | ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y1 @ Y2) @ (Y0 @ Y3)))))))))))) = $false)),
% 1.81/1.65 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.81/1.65 thf(f14,plain,(
% 1.81/1.65 ($false = ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (sK2 @ Y2 @ (Y1 @ Y2) @ (Y0 @ Y3)))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (sK2 @ Y4 @ (Y2 @ Y4) @ (Y1 @ Y3)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (sK2 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4))))))))))))))))),
% 1.81/1.65 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.81/1.65 % SZS output end Proof for DTF2THF_3007
% 1.81/1.65 % (3116)------------------------------
% 1.81/1.65 % (3116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.65 % (3116)Termination reason: Refutation
% 1.81/1.65
% 1.81/1.65 % (3116)Memory used [KB]: 6652
% 1.81/1.65 % (3116)Time elapsed: 0.147 s
% 1.81/1.65 % (3116)Instructions burned: 257 (million)
% 1.81/1.65 % (3116)------------------------------
% 1.81/1.65 % (3116)------------------------------
% 1.81/1.65 % (3104)Success in time 0.184 s
%------------------------------------------------------------------------------