%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV000^5 : 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 : n008.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 09:40:01 AM UTC 2026
% Result : Theorem 1.48s 1.38s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 97 ( 38 unt; 0 typ; 4 def)
% Number of atoms : 805 ( 324 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 2638 ( 66 ~; 60 |; 101 &;2038 @)
% ( 7 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 13 con; 0-2 aty)
% ( 324 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 473 ( 344 ^; 129 !; 0 ?; 473 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > a > a ).
thf(func_def_19,type,
sK3: a > a > a ).
thf(func_def_20,type,
sK4: a ).
thf(func_def_21,type,
sK5: a ).
thf(func_def_22,type,
sK6: a ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: a ).
thf(func_def_25,type,
sK9: a ).
thf(f564,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f35,f39,f486,f558]) ).
thf(f558,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f557]) ).
thf(f557,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f556]) ).
thf(f556,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f555]) ).
thf(f555,plain,
( ( ( ( sK2 @ sK9 @ sK8 )
= ( sK2 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f517,f547]) ).
thf(f547,plain,
! [X0: a,X1: a] :
( ( sK2 @ X0 @ ( sK2 @ X0 @ X1 ) )
= ( sK2 @ X0 @ X1 ) ),
inference(superposition,[status(thm)],[f79,f537]) ).
thf(f537,plain,
! [X0: a] :
( ( sK2 @ X0 @ X0 )
= X0 ),
inference(superposition,[status(thm)],[f531,f60]) ).
thf(f60,plain,
! [X1: a] :
( ( sK3 @ X1 @ X1 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: a] :
( $true
= ( ( sK3 @ X1 @ X1 )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
= ( sK3 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
= ( sK3 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > a] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
= ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( sK2 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( sK2 @ Y1 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ Y1 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( Y0 @ Y2 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ ( sK2 @ Y3 @ Y2 ) @ Y1 )
= ( sK2 @ Y3 @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
= Y1 ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ ( Y0 @ Y1 @ ( sK2 @ Y3 @ Y2 ) ) )
= ( Y0 @ ( sK2 @ Y3 @ Y1 ) @ ( sK2 @ Y3 @ Y2 ) ) ) ) ) )
= ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y1 )
= Y1 )
=> ( ( sK2 @ Y3 @ ( Y0 @ Y2 @ Y1 ) )
= ( Y0 @ ( sK2 @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
= ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( sK2 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( sK2 @ Y1 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ Y1 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( Y0 @ Y2 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ ( sK2 @ Y3 @ Y2 ) @ Y1 )
= ( sK2 @ Y3 @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
= Y1 ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ ( Y0 @ Y1 @ ( sK2 @ Y3 @ Y2 ) ) )
= ( Y0 @ ( sK2 @ Y3 @ Y1 ) @ ( sK2 @ Y3 @ Y2 ) ) ) ) ) )
= ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y1 )
= Y1 )
=> ( ( sK2 @ Y3 @ ( Y0 @ Y2 @ Y1 ) )
= ( Y0 @ ( sK2 @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > a] :
( !! @ ( a > a > a )
@ ^ [Y1: a > a > a] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
= ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y2 @ Y3 ) @ Y3 )
= Y3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ Y2 @ ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ ( Y1 @ Y2 @ ( Y0 @ Y4 @ Y3 ) ) )
= ( Y1 @ ( Y0 @ Y4 @ Y2 ) @ ( Y0 @ Y4 @ Y3 ) ) ) ) ) )
= ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
= Y2 )
=> ( ( Y0 @ Y4 @ ( Y1 @ Y3 @ Y2 ) )
= ( Y1 @ ( Y0 @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( !! @ ( a > a > a )
@ ^ [Y1: a > a > a] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
= ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y2 @ Y3 ) @ Y3 )
= Y3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ Y2 @ ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ ( Y1 @ Y2 @ ( Y0 @ Y4 @ Y3 ) ) )
= ( Y1 @ ( Y0 @ Y4 @ Y2 ) @ ( Y0 @ Y4 @ Y3 ) ) ) ) ) )
= ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
= Y2 )
=> ( ( Y0 @ Y4 @ ( Y1 @ Y3 @ Y2 ) )
= ( Y1 @ ( Y0 @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( !! @ ( a > a > a )
@ ^ [Y1: a > a > a] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
= ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y2 @ Y3 ) @ Y3 )
= Y3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ Y2 @ ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ ( Y1 @ Y2 @ ( Y0 @ Y4 @ Y3 ) ) )
= ( Y1 @ ( Y0 @ Y4 @ Y2 ) @ ( Y0 @ Y4 @ Y3 ) ) ) ) ) )
= ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
= Y2 )
=> ( ( Y0 @ Y4 @ ( Y1 @ Y3 @ Y2 ) )
= ( Y1 @ ( Y0 @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( !! @ ( a > a > a )
@ ^ [Y1: a > a > a] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
= ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y2 @ Y3 ) @ Y3 )
= Y3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ Y2 @ ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ ( Y1 @ Y2 @ ( Y0 @ Y4 @ Y3 ) ) )
= ( Y1 @ ( Y0 @ Y4 @ Y2 ) @ ( Y0 @ Y4 @ Y3 ) ) ) ) ) )
= ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
= Y2 )
=> ( ( Y0 @ Y4 @ ( Y1 @ Y3 @ Y2 ) )
= ( Y1 @ ( Y0 @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 )
& ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
& ! [X6: a,X7: a] :
( ( X1 @ ( X0 @ X6 @ X7 ) @ X7 )
= X7 )
& ! [X8: a,X9: a,X10: a] :
( ( X0 @ ( X0 @ X10 @ X9 ) @ X8 )
= ( X0 @ X10 @ ( X0 @ X9 @ X8 ) ) )
& ! [X11: a,X12: a] :
( ( X0 @ ( X1 @ X12 @ X11 ) @ X11 )
= X11 )
& ! [X13: a,X14: a] :
( ( X1 @ X14 @ X13 )
= ( X1 @ X13 @ X14 ) )
& ! [X15: a,X16: a] :
( ( X0 @ X15 @ X16 )
= ( X0 @ X16 @ X15 ) )
& ! [X17: a] :
( ( X1 @ X17 @ X17 )
= X17 ) )
=> ( ! [X18: a,X19: a,X20: a] :
( ( X1 @ X18 @ ( X0 @ X20 @ ( X1 @ X18 @ X19 ) ) )
= ( X0 @ ( X1 @ X18 @ X20 ) @ ( X1 @ X18 @ X19 ) ) )
<=> ! [X21: a,X22: a,X23: a] :
( ( ( X1 @ X21 @ X23 )
= X23 )
=> ( ( X1 @ X21 @ ( X0 @ X22 @ X23 ) )
= ( X0 @ ( X1 @ X21 @ X22 ) @ X23 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > a,X0: a > a > a] :
( ( ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 )
& ! [X2: a,X3: a,X4: a] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( X0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X4: a,X3: a,X2: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X3: a,X2: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
= ( X0 @ X3 @ X2 ) )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 ) )
=> ( ! [X2: a,X4: a,X3: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ ( X0 @ X2 @ X4 ) ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) )
<=> ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X4 )
= X4 )
=> ( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > a,X0: a > a > a] :
( ( ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 )
& ! [X2: a,X3: a,X4: a] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( X0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X4: a,X3: a,X2: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X3: a,X2: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
= ( X0 @ X3 @ X2 ) )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 ) )
=> ( ! [X2: a,X4: a,X3: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ ( X0 @ X2 @ X4 ) ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) )
<=> ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X4 )
= X4 )
=> ( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.I5t9o6d3QE/DTF2THF_3622.p',cMODULAR_EQUIV_THM_pme) ).
thf(f531,plain,
! [X2: a,X1: a] :
( ( sK2 @ ( sK3 @ X2 @ X1 ) @ X1 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f530]) ).
thf(f530,plain,
! [X2: a,X1: a] :
( ( ( sK2 @ ( sK3 @ X2 @ X1 ) @ X1 )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f529]) ).
thf(f529,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ ( sK3 @ Y0 @ X1 ) @ X1 )
= X1 )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f528]) ).
thf(f528,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ ( sK3 @ Y0 @ X1 ) @ X1 )
= X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f527]) ).
thf(f527,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f523]) ).
thf(f523,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f522]) ).
thf(f522,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f57,f521]) ).
thf(f521,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
= ( sK3 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
= ( sK3 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
= ( sK3 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f52]) ).
thf(f52,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
= ( sK3 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f15,f50]) ).
thf(f79,plain,
! [X2: a,X3: a,X1: a] :
( ( sK2 @ ( sK2 @ X3 @ X2 ) @ X1 )
= ( sK2 @ X3 @ ( sK2 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( sK2 @ ( sK2 @ X3 @ X2 ) @ X1 )
= ( sK2 @ X3 @ ( sK2 @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ ( sK2 @ Y0 @ X2 ) @ X1 )
= ( sK2 @ Y0 @ ( sK2 @ X2 @ X1 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ ( sK2 @ Y0 @ X2 ) @ X1 )
= ( sK2 @ Y0 @ ( sK2 @ X2 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK2 @ Y1 @ Y0 ) @ X1 )
= ( sK2 @ Y1 @ ( sK2 @ Y0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK2 @ Y1 @ Y0 ) @ X1 )
= ( sK2 @ Y1 @ ( sK2 @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f53,f57]) ).
thf(f517,plain,
( ( ( ( sK2 @ sK9 @ ( sK2 @ sK9 @ sK8 ) )
= ( sK2 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f510]) ).
thf(f510,plain,
( ( ( ( sK2 @ sK9 @ ( sK2 @ sK9 @ sK8 ) )
!= ( sK2 @ sK9 @ sK8 ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f508]) ).
thf(f508,plain,
( ( $true
= ( ( ( sK2 @ sK9 @ ( sK2 @ sK9 @ sK8 ) )
= ( sK2 @ sK9 @ sK8 ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f502,f495]) ).
thf(f495,plain,
( ( ( ( sK2 @ sK9 @ ( sK3 @ sK7 @ ( sK2 @ sK9 @ sK8 ) ) )
= ( sK3 @ ( sK2 @ sK9 @ sK7 ) @ ( sK2 @ sK9 @ sK8 ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f494]) ).
thf(f494,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ ( sK3 @ sK7 @ ( sK2 @ Y0 @ sK8 ) ) )
= ( sK3 @ ( sK2 @ Y0 @ sK7 ) @ ( sK2 @ Y0 @ sK8 ) ) )
@ sK9 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f493]) ).
thf(f493,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ ( sK3 @ sK7 @ ( sK2 @ Y0 @ sK8 ) ) )
= ( sK3 @ ( sK2 @ Y0 @ sK7 ) @ ( sK2 @ Y0 @ sK8 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f492]) ).
thf(f492,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ ( sK3 @ sK7 @ ( sK2 @ Y1 @ Y0 ) ) )
= ( sK3 @ ( sK2 @ Y1 @ sK7 ) @ ( sK2 @ Y1 @ Y0 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f491]) ).
thf(f491,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ ( sK3 @ sK7 @ ( sK2 @ Y1 @ Y0 ) ) )
= ( sK3 @ ( sK2 @ Y1 @ sK7 ) @ ( sK2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f490]) ).
thf(f490,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl0_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f502,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK2 @ X3 @ X1 )
= X1 )
=> ( ( sK2 @ X3 @ ( sK3 @ X2 @ X1 ) )
= ( sK3 @ ( sK2 @ X3 @ X2 ) @ X1 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f501]) ).
thf(f501,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
= X1 )
=> ( ( sK2 @ Y0 @ ( sK3 @ X2 @ X1 ) )
= ( sK3 @ ( sK2 @ Y0 @ X2 ) @ X1 ) ) )
@ X3 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f500]) ).
thf(f500,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
= X1 )
=> ( ( sK2 @ Y0 @ ( sK3 @ X2 @ X1 ) )
= ( sK3 @ ( sK2 @ Y0 @ X2 ) @ X1 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f499]) ).
thf(f499,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ X1 )
= X1 )
=> ( ( sK2 @ Y1 @ ( sK3 @ Y0 @ X1 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ X1 ) ) ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f498]) ).
thf(f498,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ X1 )
= X1 )
=> ( ( sK2 @ Y1 @ ( sK3 @ Y0 @ X1 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ X1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f497]) ).
thf(f497,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f486,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f485]) ).
thf(f485,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f484]) ).
thf(f484,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f483]) ).
thf(f483,plain,
( ( ( ( sK2 @ sK6 @ ( sK3 @ sK5 @ sK4 ) )
= ( sK2 @ sK6 @ ( sK3 @ sK5 @ sK4 ) ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f457,f462]) ).
thf(f462,plain,
( ! [X0: a] :
( ( sK3 @ ( sK2 @ sK6 @ X0 ) @ sK4 )
= ( sK2 @ sK6 @ ( sK3 @ X0 @ sK4 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f47,f458]) ).
thf(f458,plain,
( ( ( sK2 @ sK6 @ sK4 )
= sK4 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f455]) ).
thf(f455,plain,
( ( ( ( sK2 @ sK6 @ sK4 )
= sK4 )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f377]) ).
thf(f377,plain,
( ( ( ( ( sK2 @ sK6 @ sK4 )
= sK4 )
=> ( ( sK2 @ sK6 @ ( sK3 @ sK5 @ sK4 ) )
= ( sK3 @ ( sK2 @ sK6 @ sK5 ) @ sK4 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f376]) ).
thf(f376,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK4 )
= sK4 )
=> ( ( sK2 @ Y0 @ ( sK3 @ sK5 @ sK4 ) )
= ( sK3 @ ( sK2 @ Y0 @ sK5 ) @ sK4 ) ) )
@ sK6 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f323]) ).
thf(f323,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK4 )
= sK4 )
=> ( ( sK2 @ Y0 @ ( sK3 @ sK5 @ sK4 ) )
= ( sK3 @ ( sK2 @ Y0 @ sK5 ) @ sK4 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f322]) ).
thf(f322,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ sK4 )
= sK4 )
=> ( ( sK2 @ Y1 @ ( sK3 @ Y0 @ sK4 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ sK4 ) ) ) )
@ sK5 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f265]) ).
thf(f265,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ sK4 )
= sK4 )
=> ( ( sK2 @ Y1 @ ( sK3 @ Y0 @ sK4 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ sK4 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f264]) ).
thf(f264,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
@ sK4 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f47,plain,
( ! [X2: a,X3: a,X1: a] :
( ( sK3 @ ( sK2 @ X3 @ X1 ) @ ( sK2 @ X3 @ X2 ) )
= ( sK2 @ X3 @ ( sK3 @ X1 @ ( sK2 @ X3 @ X2 ) ) ) )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( sK2 @ X3 @ ( sK3 @ X1 @ ( sK2 @ X3 @ X2 ) ) )
= ( sK3 @ ( sK2 @ X3 @ X1 ) @ ( sK2 @ X3 @ X2 ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ ( sK3 @ X1 @ ( sK2 @ Y0 @ X2 ) ) )
= ( sK3 @ ( sK2 @ Y0 @ X1 ) @ ( sK2 @ Y0 @ X2 ) ) )
@ X3 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ ( sK3 @ X1 @ ( sK2 @ Y0 @ X2 ) ) )
= ( sK3 @ ( sK2 @ Y0 @ X1 ) @ ( sK2 @ Y0 @ X2 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ ( sK3 @ X1 @ ( sK2 @ Y1 @ Y0 ) ) )
= ( sK3 @ ( sK2 @ Y1 @ X1 ) @ ( sK2 @ Y1 @ Y0 ) ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ ( sK3 @ X1 @ ( sK2 @ Y1 @ Y0 ) ) )
= ( sK3 @ ( sK2 @ Y1 @ X1 ) @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
!= $false )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f16,f24]) ).
thf(f16,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
!= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f457,plain,
( ( ( ( sK2 @ sK6 @ ( sK3 @ sK5 @ sK4 ) )
= ( sK3 @ ( sK2 @ sK6 @ sK5 ) @ sK4 ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f456]) ).
thf(f456,plain,
( ( ( $true
=> ( ( sK2 @ sK6 @ ( sK3 @ sK5 @ sK4 ) )
= ( sK3 @ ( sK2 @ sK6 @ sK5 ) @ sK4 ) ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f377,f455]) ).
thf(f39,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f31,f27]) ).
thf(f31,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f35,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f20,f33,f30]) ).
thf(f20,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f28,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f26,f23]) ).
thf(f21,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y2 @ ( sK3 @ Y1 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ ( sK3 @ Y0 @ ( sK2 @ Y2 @ Y1 ) ) )
= ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV000^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n008.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:39:39 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.41 thf(spec,logic,$$dhol).
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : SEV000^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.41 % Domain : Set Theory (Relations)
% 0.15/0.41 % Problem : TPS problem MODULAR-EQUIV-THM
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English : The equivalence of two definitions of modularity.
% 0.15/0.41
% 0.15/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.41 % Source : [Bro09]
% 0.15/0.41 % Names : tps_0562 [Bro09]
% 0.15/0.41 % : MODULAR-EQUIV-THM [TPS]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 1.00 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.15/0.41 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.15/0.41 % Number of atoms : 11 ( 11 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 11 ( 11 avg)
% 0.15/0.41 % Number of connectives : 68 ( 0 ~; 0 |; 7 &; 58 @)
% 0.15/0.41 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 13 ( 13 avg)
% 0.15/0.41 % Number of types : 1 ( 1 usr)
% 0.15/0.41 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.15/0.41 % Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% 0.15/0.41 % SPC : TH0_THM_EQU_NAR
% 0.15/0.41
% 0.15/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.41 % : Polymorphic definitions expanded.
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 thf(a_type,type,
% 0.15/0.41 a: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(cMODULAR_EQUIV_THM_pme,conjecture,
% 0.15/0.41 ! [JOIN: a > a > a,MEET: a > a > a] :
% 0.15/0.41 ( ( ! [Xx: a] :
% 0.15/0.41 ( ( JOIN @ Xx @ Xx )
% 0.15/0.41 = Xx )
% 0.15/0.41 & ! [Xx: a] :
% 0.15/0.41 ( ( MEET @ Xx @ Xx )
% 0.15/0.41 = Xx )
% 0.15/0.41 & ! [Xx: a,Xy: a,Xz: a] :
% 0.15/0.41 ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
% 0.15/0.41 = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
% 0.15/0.41 & ! [Xx: a,Xy: a,Xz: a] :
% 0.15/0.41 ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
% 0.15/0.41 = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
% 0.15/0.41 & ! [Xx: a,Xy: a] :
% 0.15/0.41 ( ( JOIN @ Xx @ Xy )
% 0.15/0.41 = ( JOIN @ Xy @ Xx ) )
% 0.15/0.41 & ! [Xx: a,Xy: a] :
% 0.15/0.41 ( ( MEET @ Xx @ Xy )
% 0.15/0.41 = ( MEET @ Xy @ Xx ) )
% 0.15/0.41 & ! [Xx: a,Xy: a] :
% 0.15/0.41 ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
% 0.15/0.41 = Xy )
% 0.15/0.41 & ! [Xx: a,Xy: a] :
% 0.15/0.41 ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
% 0.15/0.41 = Xy ) )
% 0.15/0.41 => ( ! [Xx: a,Xy: a,Xz: a] :
% 0.15/0.41 ( ( ( JOIN @ Xx @ Xz )
% 0.15/0.41 = Xz )
% 0.15/0.41 => ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 0.15/0.41 = ( MEET @ ( JOIN @ Xx @ Xy ) @ Xz ) ) )
% 0.15/0.41 <=> ! [Xx: a,Xy: a,Xz: a] :
% 0.15/0.41 ( ( JOIN @ Xx @ ( MEET @ Xy @ ( JOIN @ Xx @ Xz ) ) )
% 0.15/0.41 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------------------------
% 1.38/1.24 ---- Embedded in THF ---
% 1.38/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.24 %%% Generated on Tue Feb 24 12:39:40 EST 2026
% 1.38/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.24 %%% Logic specification used:
% 1.38/1.24 %%% thf(spec, logic, $$dhol).
% 1.38/1.24
% 1.38/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.I5t9o6d3QE/DTF2DTF3622.p
% See solution above
% 1.38/1.24 ------------------------
% 1.38/1.24 ---- Cleaned THF ---
% 1.38/1.24 thf(a_type,type,
% 1.38/1.24 a: $tType ).
% 1.38/1.24
% 1.38/1.24 thf(cMODULAR_EQUIV_THM_pme,conjecture,
% 1.38/1.24 ! [JOIN: a > a > a,MEET: a > a > a] :
% 1.38/1.24 ( ( ! [Xx: a] :
% 1.38/1.24 ( ( JOIN @ Xx @ Xx )
% 1.38/1.24 = Xx )
% 1.38/1.24 & ! [Xx: a] :
% 1.38/1.24 ( ( MEET @ Xx @ Xx )
% 1.38/1.24 = Xx )
% 1.38/1.24 & ! [Xx: a,Xy: a,Xz: a] :
% 1.38/1.24 ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
% 1.38/1.24 = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
% 1.38/1.24 & ! [Xx: a,Xy: a,Xz: a] :
% 1.38/1.24 ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
% 1.38/1.24 = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
% 1.38/1.24 & ! [Xx: a,Xy: a] :
% 1.38/1.24 ( ( JOIN @ Xx @ Xy )
% 1.38/1.24 = ( JOIN @ Xy @ Xx ) )
% 1.38/1.24 & ! [Xx: a,Xy: a] :
% 1.38/1.24 ( ( MEET @ Xx @ Xy )
% 1.38/1.24 = ( MEET @ Xy @ Xx ) )
% 1.38/1.24 & ! [Xx: a,Xy: a] :
% 1.38/1.24 ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
% 1.38/1.24 = Xy )
% 1.38/1.24 & ! [Xx: a,Xy: a] :
% 1.38/1.24 ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
% 1.38/1.24 = Xy ) )
% 1.38/1.24 => ( ! [Xx: a,Xy: a,Xz: a] :
% 1.38/1.24 ( ( ( JOIN @ Xx @ Xz )
% 1.38/1.24 = Xz )
% 1.38/1.24 => ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 1.38/1.24 = ( MEET @ ( JOIN @ Xx @ Xy ) @ Xz ) ) )
% 1.38/1.24 <=> ! [Xx: a,Xy: a,Xz: a] :
% 1.38/1.24 ( ( JOIN @ Xx @ ( MEET @ Xy @ ( JOIN @ Xx @ Xz ) ) )
% 1.38/1.24 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) ) ) ) ).
% 1.38/1.24 ------------------------
% 1.38/1.26 % (3759)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3622 for (3000ds/18Mi)
% 1.38/1.26 % (3758)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_3622 for (3000ds/275Mi)
% 1.38/1.26 % (3757)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_3622 for (3000ds/2Mi)
% 1.38/1.26 % (3753)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_3622 for (3000ds/4Mi)
% 1.38/1.26 % (3754)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_3622 for (3000ds/27Mi)
% 1.38/1.26 % (3756)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3622 for (3000ds/2Mi)
% 1.38/1.26 % (3752)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3622 for (3000ds/183Mi)
% 1.38/1.26 % (3757)Instruction limit reached!
% 1.38/1.26 % (3757)------------------------------
% 1.38/1.26 % (3757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.26 % (3757)Termination reason: Unknown
% 1.38/1.26 % (3757)Termination phase: shuffling
% 1.38/1.26
% 1.38/1.26 % (3757)Memory used [KB]: 895
% 1.38/1.26 % (3757)Time elapsed: 0.002 s
% 1.38/1.26 % (3757)Instructions burned: 2 (million)
% 1.38/1.26 % (3757)------------------------------
% 1.38/1.26 % (3757)------------------------------
% 1.38/1.26 % (3756)Instruction limit reached!
% 1.38/1.26 % (3756)------------------------------
% 1.38/1.26 % (3756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.26 % (3756)Termination reason: Unknown
% 1.38/1.26 % (3756)Termination phase: Saturation
% 1.38/1.26
% 1.38/1.26 % (3756)Memory used [KB]: 5500
% 1.38/1.26 % (3756)Time elapsed: 0.003 s
% 1.38/1.26 % (3756)Instructions burned: 4 (million)
% 1.38/1.26 % (3756)------------------------------
% 1.38/1.26 % (3756)------------------------------
% 1.38/1.26 % (3753)Instruction limit reached!
% 1.38/1.26 % (3753)------------------------------
% 1.38/1.26 % (3753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.26 % (3753)Termination reason: Unknown
% 1.38/1.26 % (3753)Termination phase: Saturation
% 1.38/1.26
% 1.38/1.26 % (3753)Memory used [KB]: 5500
% 1.38/1.26 % (3753)Time elapsed: 0.004 s
% 1.38/1.26 % (3753)Instructions burned: 6 (million)
% 1.38/1.26 % (3753)------------------------------
% 1.38/1.26 % (3753)------------------------------
% 1.38/1.26 % (3759)Instruction limit reached!
% 1.38/1.26 % (3759)------------------------------
% 1.38/1.26 % (3759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.26 % (3759)Termination reason: Unknown
% 1.38/1.26 % (3759)Termination phase: Saturation
% 1.38/1.26
% 1.38/1.26 % (3759)Memory used [KB]: 5628
% 1.38/1.26 % (3759)Time elapsed: 0.008 s
% 1.38/1.26 % (3759)Instructions burned: 20 (million)
% 1.38/1.26 % (3759)------------------------------
% 1.38/1.26 % (3759)------------------------------
% 1.38/1.27 % (3754)Instruction limit reached!
% 1.38/1.27 % (3754)------------------------------
% 1.38/1.27 % (3754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.27 % (3754)Termination reason: Unknown
% 1.38/1.27 % (3754)Termination phase: Saturation
% 1.38/1.27
% 1.38/1.27 % (3754)Memory used [KB]: 5628
% 1.38/1.27 % (3754)Time elapsed: 0.011 s
% 1.38/1.27 % (3754)Instructions burned: 29 (million)
% 1.38/1.27 % (3754)------------------------------
% 1.38/1.27 % (3754)------------------------------
% 1.38/1.27 % (3766)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/3Mi)
% 1.38/1.27 % (3768)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_3622 for (2999ds/37Mi)
% 1.38/1.27 % (3766)Instruction limit reached!
% 1.38/1.27 % (3766)------------------------------
% 1.38/1.27 % (3766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.27 % (3766)Termination reason: Unknown
% 1.38/1.27 % (3766)Termination phase: Saturation
% 1.38/1.27
% 1.38/1.27 % (3766)Memory used [KB]: 5500
% 1.38/1.27 % (3766)Time elapsed: 0.002 s
% 1.38/1.27 % (3766)Instructions burned: 4 (million)
% 1.38/1.27 % (3766)------------------------------
% 1.38/1.27 % (3766)------------------------------
% 1.38/1.27 % (3769)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_3622 for (2999ds/15Mi)
% 1.38/1.27 % (3772)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_3622 for (2999ds/3Mi)
% 1.38/1.27 % (3769)Instruction limit reached!
% 1.38/1.27 % (3769)------------------------------
% 1.38/1.27 % (3769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.27 % (3769)Termination reason: Unknown
% 1.38/1.27 % (3769)Termination phase: Saturation
% 1.38/1.27
% 1.38/1.27 % (3769)Memory used [KB]: 5628
% 1.38/1.27 % (3769)Time elapsed: 0.006 s
% 1.38/1.27 % (3769)Instructions burned: 15 (million)
% 1.38/1.27 % (3769)------------------------------
% 1.38/1.27 % (3769)------------------------------
% 1.38/1.27 % (3772)Instruction limit reached!
% 1.38/1.27 % (3772)------------------------------
% 1.38/1.27 % (3772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.27 % (3772)Termination reason: Unknown
% 1.38/1.27 % (3772)Termination phase: Preprocessing 3
% 1.38/1.27
% 1.38/1.27 % (3772)Memory used [KB]: 1023
% 1.38/1.27 % (3772)Time elapsed: 0.002 s
% 1.38/1.27 % (3772)Instructions burned: 3 (million)
% 1.38/1.27 % (3772)------------------------------
% 1.38/1.27 % (3772)------------------------------
% 1.38/1.27 % (3775)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_3622 for (2999ds/1041Mi)
% 1.38/1.28 % (3777)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/7Mi)
% 1.38/1.28 % (3768)Instruction limit reached!
% 1.38/1.28 % (3768)------------------------------
% 1.38/1.28 % (3768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.28 % (3768)Termination reason: Unknown
% 1.38/1.28 % (3768)Termination phase: Saturation
% 1.38/1.28
% 1.38/1.28 % (3768)Memory used [KB]: 5628
% 1.38/1.28 % (3768)Time elapsed: 0.013 s
% 1.38/1.28 % (3768)Instructions burned: 39 (million)
% 1.38/1.28 % (3768)------------------------------
% 1.38/1.28 % (3768)------------------------------
% 1.38/1.28 % (3777)Instruction limit reached!
% 1.38/1.28 % (3777)------------------------------
% 1.38/1.28 % (3777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.28 % (3777)Termination reason: Unknown
% 1.38/1.28 % (3777)Termination phase: Saturation
% 1.38/1.28
% 1.38/1.28 % (3777)Memory used [KB]: 1023
% 1.38/1.28 % (3777)Time elapsed: 0.004 s
% 1.38/1.28 % (3777)Instructions burned: 9 (million)
% 1.38/1.28 % (3777)------------------------------
% 1.38/1.28 % (3777)------------------------------
% 1.38/1.28 % (3779)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/16Mi)
% 1.38/1.28 % (3780)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_3622 for (2999ds/3Mi)
% 1.38/1.28 % (3780)Instruction limit reached!
% 1.38/1.28 % (3780)------------------------------
% 1.38/1.28 % (3780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.28 % (3780)Termination reason: Unknown
% 1.38/1.28 % (3780)Termination phase: Property scanning
% 1.38/1.28
% 1.38/1.28 % (3780)Memory used [KB]: 1023
% 1.38/1.28 % (3780)Time elapsed: 0.002 s
% 1.38/1.28 % (3780)Instructions burned: 3 (million)
% 1.38/1.28 % (3780)------------------------------
% 1.38/1.28 % (3780)------------------------------
% 1.38/1.29 % (3779)Instruction limit reached!
% 1.38/1.29 % (3779)------------------------------
% 1.38/1.29 % (3779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.29 % (3779)Termination reason: Unknown
% 1.38/1.29 % (3779)Termination phase: Saturation
% 1.38/1.29
% 1.38/1.29 % (3779)Memory used [KB]: 5756
% 1.38/1.29 % (3779)Time elapsed: 0.007 s
% 1.38/1.29 % (3779)Instructions burned: 18 (million)
% 1.38/1.29 % (3779)------------------------------
% 1.38/1.29 % (3779)------------------------------
% 1.38/1.29 % (3782)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_3622 for (2999ds/3Mi)
% 1.38/1.29 % (3783)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/7Mi)
% 1.38/1.29 % (3782)Instruction limit reached!
% 1.38/1.29 % (3782)------------------------------
% 1.38/1.29 % (3782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.29 % (3782)Termination reason: Unknown
% 1.38/1.29 % (3782)Termination phase: Preprocessing 3
% 1.38/1.29
% 1.38/1.29 % (3782)Memory used [KB]: 1023
% 1.38/1.29 % (3782)Time elapsed: 0.002 s
% 1.38/1.29 % (3782)Instructions burned: 3 (million)
% 1.38/1.29 % (3782)------------------------------
% 1.38/1.29 % (3782)------------------------------
% 1.38/1.29 % (3783)Refutation not found, incomplete strategy
% 1.38/1.29 % (3783)------------------------------
% 1.38/1.29 % (3783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.29 % (3783)Termination reason: Refutation not found, incomplete strategy
% 1.38/1.29
% 1.38/1.29
% 1.38/1.29 % (3783)Memory used [KB]: 5500
% 1.38/1.29 % (3783)Time elapsed: 0.003 s
% 1.38/1.29 % (3783)Instructions burned: 6 (million)
% 1.38/1.29 % (3783)------------------------------
% 1.38/1.29 % (3783)------------------------------
% 1.38/1.29 % (3786)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/3Mi)
% 1.38/1.29 % (3786)Instruction limit reached!
% 1.38/1.29 % (3786)------------------------------
% 1.38/1.29 % (3786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.29 % (3786)Termination reason: Unknown
% 1.38/1.29 % (3786)Termination phase: Property scanning
% 1.38/1.29
% 1.38/1.29 % (3786)Memory used [KB]: 1023
% 1.38/1.29 % (3786)Time elapsed: 0.002 s
% 1.38/1.29 % (3786)Instructions burned: 4 (million)
% 1.38/1.29 % (3786)------------------------------
% 1.38/1.29 % (3786)------------------------------
% 1.48/1.30 % (3789)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/4Mi)
% 1.48/1.30 % (3791)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/18Mi)
% 1.48/1.30 % (3789)Instruction limit reached!
% 1.48/1.30 % (3789)------------------------------
% 1.48/1.30 % (3789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.30 % (3789)Termination reason: Unknown
% 1.48/1.30 % (3789)Termination phase: Saturation
% 1.48/1.30
% 1.48/1.30 % (3789)Memory used [KB]: 5500
% 1.48/1.30 % (3789)Time elapsed: 0.003 s
% 1.48/1.30 % (3789)Instructions burned: 5 (million)
% 1.48/1.30 % (3789)------------------------------
% 1.48/1.30 % (3789)------------------------------
% 1.48/1.30 % (3793)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/710Mi)
% 1.48/1.30 % (3795)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/6Mi)
% 1.48/1.30 % (3795)Instruction limit reached!
% 1.48/1.30 % (3795)------------------------------
% 1.48/1.30 % (3795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.30 % (3795)Termination reason: Unknown
% 1.48/1.30 % (3795)Termination phase: Saturation
% 1.48/1.30
% 1.48/1.30 % (3795)Memory used [KB]: 5500
% 1.48/1.30 % (3795)Time elapsed: 0.003 s
% 1.48/1.30 % (3795)Instructions burned: 6 (million)
% 1.48/1.30 % (3795)------------------------------
% 1.48/1.30 % (3795)------------------------------
% 1.48/1.31 % (3791)Instruction limit reached!
% 1.48/1.31 % (3791)------------------------------
% 1.48/1.31 % (3791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.31 % (3791)Termination reason: Unknown
% 1.48/1.31 % (3791)Termination phase: Saturation
% 1.48/1.31
% 1.48/1.31 % (3791)Memory used [KB]: 5628
% 1.48/1.31 % (3791)Time elapsed: 0.008 s
% 1.48/1.31 % (3791)Instructions burned: 20 (million)
% 1.48/1.31 % (3791)------------------------------
% 1.48/1.31 % (3791)------------------------------
% 1.48/1.31 % (3799)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_3622 for (2999ds/902Mi)
% 1.48/1.31 % (3752)Instruction limit reached!
% 1.48/1.31 % (3752)------------------------------
% 1.48/1.31 % (3752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.31 % (3752)Termination reason: Unknown
% 1.48/1.31 % (3752)Termination phase: Saturation
% 1.48/1.31
% 1.48/1.31 % (3752)Memory used [KB]: 6524
% 1.48/1.31 % (3752)Time elapsed: 0.058 s
% 1.48/1.31 % (3752)Instructions burned: 183 (million)
% 1.48/1.31 % (3752)------------------------------
% 1.48/1.31 % (3752)------------------------------
% 1.48/1.31 % (3802)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_3622 for (2999ds/21Mi)
% 1.48/1.31 % (3803)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/5Mi)
% 1.48/1.32 % (3803)Instruction limit reached!
% 1.48/1.32 % (3803)------------------------------
% 1.48/1.32 % (3803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.32 % (3803)Termination reason: Unknown
% 1.48/1.32 % (3803)Termination phase: Saturation
% 1.48/1.32
% 1.48/1.32 % (3803)Memory used [KB]: 5500
% 1.48/1.32 % (3803)Time elapsed: 0.003 s
% 1.48/1.32 % (3803)Instructions burned: 7 (million)
% 1.48/1.32 % (3803)------------------------------
% 1.48/1.32 % (3803)------------------------------
% 1.48/1.32 % (3807)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_3622 for (2999ds/6Mi)
% 1.48/1.32 % (3802)Instruction limit reached!
% 1.48/1.32 % (3802)------------------------------
% 1.48/1.32 % (3802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.32 % (3802)Termination reason: Unknown
% 1.48/1.32 % (3802)Termination phase: Saturation
% 1.48/1.32
% 1.48/1.32 % (3802)Memory used [KB]: 5628
% 1.48/1.32 % (3802)Time elapsed: 0.009 s
% 1.48/1.32 % (3802)Instructions burned: 23 (million)
% 1.48/1.32 % (3802)------------------------------
% 1.48/1.32 % (3802)------------------------------
% 1.48/1.32 % (3807)Instruction limit reached!
% 1.48/1.32 % (3807)------------------------------
% 1.48/1.32 % (3807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.32 % (3807)Termination reason: Unknown
% 1.48/1.32 % (3807)Termination phase: Saturation
% 1.48/1.32
% 1.48/1.32 % (3807)Memory used [KB]: 5500
% 1.48/1.32 % (3807)Time elapsed: 0.003 s
% 1.48/1.32 % (3807)Instructions burned: 7 (million)
% 1.48/1.32 % (3807)------------------------------
% 1.48/1.32 % (3807)------------------------------
% 1.48/1.33 % (3809)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/377Mi)
% 1.48/1.33 % (3810)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_3622 for (2999ds/779Mi)
% 1.48/1.33 % (3811)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_3622 for (2999ds/19Mi)
% 1.48/1.34 % (3758)Instruction limit reached!
% 1.48/1.34 % (3758)------------------------------
% 1.48/1.34 % (3758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.34 % (3758)Termination reason: Unknown
% 1.48/1.34 % (3758)Termination phase: Saturation
% 1.48/1.34
% 1.48/1.34 % (3758)Memory used [KB]: 6140
% 1.48/1.34 % (3758)Time elapsed: 0.083 s
% 1.48/1.34 % (3758)Instructions burned: 278 (million)
% 1.48/1.34 % (3758)------------------------------
% 1.48/1.34 % (3758)------------------------------
% 1.48/1.34 % (3811)Instruction limit reached!
% 1.48/1.34 % (3811)------------------------------
% 1.48/1.34 % (3811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.34 % (3811)Termination reason: Unknown
% 1.48/1.34 % (3811)Termination phase: Saturation
% 1.48/1.34
% 1.48/1.34 % (3811)Memory used [KB]: 5500
% 1.48/1.34 % (3811)Time elapsed: 0.007 s
% 1.48/1.34 % (3811)Instructions burned: 21 (million)
% 1.48/1.34 % (3811)------------------------------
% 1.48/1.34 % (3811)------------------------------
% 1.48/1.35 % (3820)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/879Mi)
% 1.48/1.35 % (3822)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/17Mi)
% 1.48/1.35 % (3822)Instruction limit reached!
% 1.48/1.35 % (3822)------------------------------
% 1.48/1.35 % (3822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.35 % (3822)Termination reason: Unknown
% 1.48/1.35 % (3822)Termination phase: Saturation
% 1.48/1.35
% 1.48/1.35 % (3822)Memory used [KB]: 5628
% 1.48/1.35 % (3822)Time elapsed: 0.029 s
% 1.48/1.35 % (3822)Instructions burned: 17 (million)
% 1.48/1.35 % (3822)------------------------------
% 1.48/1.35 % (3822)------------------------------
% 1.48/1.36 % (3823)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3622 for (2999ds/3Mi)
% 1.48/1.36 % (3823)Instruction limit reached!
% 1.48/1.36 % (3823)------------------------------
% 1.48/1.36 % (3823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.36 % (3823)Termination reason: Unknown
% 1.48/1.36 % (3823)Termination phase: Property scanning
% 1.48/1.36
% 1.48/1.36 % (3823)Memory used [KB]: 1023
% 1.48/1.36 % (3823)Time elapsed: 0.002 s
% 1.48/1.36 % (3823)Instructions burned: 4 (million)
% 1.48/1.36 % (3823)------------------------------
% 1.48/1.36 % (3823)------------------------------
% 1.48/1.37 % (3775)First to succeed.
% 1.48/1.37 % (3834)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3622 for (2998ds/30Mi)
% 1.48/1.38 % (3775)Refutation found. Thanks to Tanya!
% 1.48/1.38 % SZS status Theorem for DTF2THF_3622
% 1.48/1.38 % SZS output start Proof for DTF2THF_3622
% 1.48/1.38 thf(type_def_5, type, a: $tType).
% 1.48/1.38 thf(func_def_0, type, a: $tType).
% 1.48/1.38 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.48/1.38 thf(func_def_18, type, sK2: a > a > a).
% 1.48/1.38 thf(func_def_19, type, sK3: a > a > a).
% 1.48/1.38 thf(func_def_20, type, sK4: a).
% 1.48/1.38 thf(func_def_21, type, sK5: a).
% 1.48/1.38 thf(func_def_22, type, sK6: a).
% 1.48/1.38 thf(func_def_23, type, sK7: a).
% 1.48/1.38 thf(func_def_24, type, sK8: a).
% 1.48/1.38 thf(func_def_25, type, sK9: a).
% 1.48/1.38 thf(f564,plain,(
% 1.48/1.38 $false),
% 1.48/1.38 inference(avatar_sat_refutation,[status(thm)],[f28,f35,f39,f486,f558])).
% 1.48/1.38 thf(f558,plain,(
% 1.48/1.38 ~spl0_2 | ~spl0_4),
% 1.48/1.38 inference(avatar_contradiction_clause,[status(thm)],[f557])).
% 1.48/1.38 thf(f557,plain,(
% 1.48/1.38 $false | (~spl0_2 | ~spl0_4)),
% 1.48/1.38 inference(trivial_inequality_removal,[status(thm)],[f556])).
% 1.48/1.38 thf(f556,plain,(
% 1.48/1.38 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 1.48/1.38 inference(boolean_simplification,[status(thm)],[f555])).
% 1.48/1.38 thf(f555,plain,(
% 1.48/1.38 (((sK2 @ sK9 @ sK8) = (sK2 @ sK9 @ sK8)) = $false) | (~spl0_2 | ~spl0_4)),
% 1.48/1.38 inference(backward_demodulation,[status(thm)],[f517,f547])).
% 1.48/1.38 thf(f547,plain,(
% 1.48/1.38 ( ! [X0 : a,X1 : a] : (((sK2 @ X0 @ (sK2 @ X0 @ X1)) = (sK2 @ X0 @ X1))) )),
% 1.48/1.38 inference(superposition,[status(thm)],[f79,f537])).
% 1.48/1.38 thf(f537,plain,(
% 1.48/1.38 ( ! [X0 : a] : (((sK2 @ X0 @ X0) = X0)) )),
% 1.48/1.38 inference(superposition,[status(thm)],[f531,f60])).
% 1.48/1.38 thf(f60,plain,(
% 1.48/1.38 ( ! [X1 : a] : (((sK3 @ X1 @ X1) = X1)) )),
% 1.48/1.38 inference(equality_proxy_clausification,[status(thm)],[f55])).
% 1.48/1.38 thf(f55,plain,(
% 1.48/1.38 ( ! [X1 : a] : (($true = ((sK3 @ X1 @ X1) = X1))) )),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.48/1.38 thf(f54,plain,(
% 1.48/1.38 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)) @ X1) = $true)) )),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f50])).
% 1.48/1.38 thf(f50,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) = $true)),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.48/1.38 thf(f15,plain,(
% 1.48/1.38 (((((((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) = (sK3 @ Y0 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y0 @ Y1) @ Y2) = (sK3 @ Y0 @ (sK3 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) = $true)),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.48/1.38 thf(f13,plain,(
% 1.48/1.38 ((((((((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) = (sK3 @ Y0 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y0 @ Y1) @ Y2) = (sK3 @ Y0 @ (sK3 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) => ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0))))))))))) = $false)),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.48/1.38 thf(f12,plain,(
% 1.48/1.38 (((^[Y0 : a > a > a]: (((((((((!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y1) = Y1))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y1) = (Y0 @ Y1 @ Y2))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (sK2 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (sK2 @ Y1 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ Y1 @ (Y0 @ Y2 @ Y3)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (Y0 @ Y2 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ (sK2 @ Y3 @ Y2) @ Y1) = (sK2 @ Y3 @ (sK2 @ Y2 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1 @ Y1) = Y1)))) => ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ (Y0 @ Y1 @ (sK2 @ Y3 @ Y2))) = (Y0 @ (sK2 @ Y3 @ Y1) @ (sK2 @ Y3 @ Y2))))))))) = (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y1) = Y1) => ((sK2 @ Y3 @ (Y0 @ Y2 @ Y1)) = (Y0 @ (sK2 @ Y3 @ Y2) @ Y1)))))))))))) @ sK3) = $false)),
% 1.48/1.38 inference(sigma_clausification,[status(thm)],[f11])).
% 1.48/1.38 thf(f11,plain,(
% 1.48/1.38 ((!! @ (a > a > a) @ (^[Y0 : a > a > a]: (((((((((!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y1) = Y1))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y1) = (Y0 @ Y1 @ Y2))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (sK2 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (sK2 @ Y1 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ Y1 @ (Y0 @ Y2 @ Y3)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (Y0 @ Y2 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ (sK2 @ Y3 @ Y2) @ Y1) = (sK2 @ Y3 @ (sK2 @ Y2 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1 @ Y1) = Y1)))) => ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ (Y0 @ Y1 @ (sK2 @ Y3 @ Y2))) = (Y0 @ (sK2 @ Y3 @ Y1) @ (sK2 @ Y3 @ Y2))))))))) = (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y1) = Y1) => ((sK2 @ Y3 @ (Y0 @ Y2 @ Y1)) = (Y0 @ (sK2 @ Y3 @ Y2) @ Y1))))))))))))) = $false)),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.48/1.38 thf(f10,plain,(
% 1.48/1.38 (((^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3 @ Y2) = (Y1 @ Y2 @ Y3))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y0 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y2 @ Y3) @ Y3) = Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y1 @ Y2 @ Y3) @ Y4) = (Y1 @ Y2 @ (Y1 @ Y3 @ Y4)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2)))) => ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4 @ (Y1 @ Y2 @ (Y0 @ Y4 @ Y3))) = (Y1 @ (Y0 @ Y4 @ Y2) @ (Y0 @ Y4 @ Y3))))))))) = (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) = Y2) => ((Y0 @ Y4 @ (Y1 @ Y3 @ Y2)) = (Y1 @ (Y0 @ Y4 @ Y3) @ Y2)))))))))))))) @ sK2) = $false)),
% 1.48/1.38 inference(sigma_clausification,[status(thm)],[f7])).
% 1.48/1.38 thf(f7,plain,(
% 1.48/1.38 ((!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3 @ Y2) = (Y1 @ Y2 @ Y3))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y0 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y2 @ Y3) @ Y3) = Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y1 @ Y2 @ Y3) @ Y4) = (Y1 @ Y2 @ (Y1 @ Y3 @ Y4)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2)))) => ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4 @ (Y1 @ Y2 @ (Y0 @ Y4 @ Y3))) = (Y1 @ (Y0 @ Y4 @ Y2) @ (Y0 @ Y4 @ Y3))))))))) = (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) = Y2) => ((Y0 @ Y4 @ (Y1 @ Y3 @ Y2)) = (Y1 @ (Y0 @ Y4 @ Y3) @ Y2))))))))))))))) = $false)),
% 1.48/1.38 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.48/1.38 thf(f6,plain,(
% 1.48/1.38 ((~ (!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3 @ Y2) = (Y1 @ Y2 @ Y3))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y0 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y2 @ Y3) @ Y3) = Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y1 @ Y2 @ Y3) @ Y4) = (Y1 @ Y2 @ (Y1 @ Y3 @ Y4)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2)))) => ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4 @ (Y1 @ Y2 @ (Y0 @ Y4 @ Y3))) = (Y1 @ (Y0 @ Y4 @ Y2) @ (Y0 @ Y4 @ Y3))))))))) = (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) = Y2) => ((Y0 @ Y4 @ (Y1 @ Y3 @ Y2)) = (Y1 @ (Y0 @ Y4 @ Y3) @ Y2)))))))))))))))) = $true)),
% 1.48/1.38 inference(cnf_transformation,[status(thm)],[f5])).
% 1.48/1.38 thf(f5,plain,(
% 1.48/1.38 ((~ (!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3 @ Y2) = (Y1 @ Y2 @ Y3))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y0 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y2 @ Y3) @ Y3) = Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y1 @ Y2 @ Y3) @ Y4) = (Y1 @ Y2 @ (Y1 @ Y3 @ Y4)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2)))) => ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4 @ (Y1 @ Y2 @ (Y0 @ Y4 @ Y3))) = (Y1 @ (Y0 @ Y4 @ Y2) @ (Y0 @ Y4 @ Y3))))))))) = (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) = Y2) => ((Y0 @ Y4 @ (Y1 @ Y3 @ Y2)) = (Y1 @ (Y0 @ Y4 @ Y3) @ Y2)))))))))))))))) = $true)),
% 1.48/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.38 thf(f4,plain,(
% 1.48/1.38 ~! [X0 : a > a > a,X1 : a > a > a] : ((! [X2 : a] : ((X0 @ X2 @ X2) = X2) & ! [X3 : a,X4 : a,X5 : a] : ((X1 @ (X1 @ X3 @ X4) @ X5) = (X1 @ X3 @ (X1 @ X4 @ X5))) & ! [X6 : a,X7 : a] : ((X1 @ (X0 @ X6 @ X7) @ X7) = X7) & ! [X8 : a,X9 : a,X10 : a] : ((X0 @ (X0 @ X10 @ X9) @ X8) = (X0 @ X10 @ (X0 @ X9 @ X8))) & ! [X11 : a,X12 : a] : ((X0 @ (X1 @ X12 @ X11) @ X11) = X11) & ! [X13 : a,X14 : a] : ((X1 @ X14 @ X13) = (X1 @ X13 @ X14)) & ! [X15 : a,X16 : a] : ((X0 @ X15 @ X16) = (X0 @ X16 @ X15)) & ! [X17 : a] : ((X1 @ X17 @ X17) = X17)) => (! [X18 : a,X19 : a,X20 : a] : ((X1 @ X18 @ (X0 @ X20 @ (X1 @ X18 @ X19))) = (X0 @ (X1 @ X18 @ X20) @ (X1 @ X18 @ X19))) <=> ! [X21 : a,X22 : a,X23 : a] : (((X1 @ X21 @ X23) = X23) => ((X1 @ X21 @ (X0 @ X22 @ X23)) = (X0 @ (X1 @ X21 @ X22) @ X23)))))),
% 1.48/1.38 inference(rectify,[status(thm)],[f2])).
% 1.48/1.38 thf(f2,negated_conjecture,(
% 1.48/1.38 ~! [X1 : a > a > a,X0 : a > a > a] : ((! [X2 : a] : ((X1 @ X2 @ X2) = X2) & ! [X2 : a,X3 : a,X4 : a] : ((X0 @ (X0 @ X2 @ X3) @ X4) = (X0 @ X2 @ (X0 @ X3 @ X4))) & ! [X2 : a,X3 : a] : ((X0 @ (X1 @ X2 @ X3) @ X3) = X3) & ! [X4 : a,X3 : a,X2 : a] : ((X1 @ (X1 @ X2 @ X3) @ X4) = (X1 @ X2 @ (X1 @ X3 @ X4))) & ! [X3 : a,X2 : a] : ((X1 @ (X0 @ X2 @ X3) @ X3) = X3) & ! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) = (X0 @ X3 @ X2)) & ! [X2 : a,X3 : a] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)) & ! [X2 : a] : ((X0 @ X2 @ X2) = X2)) => (! [X2 : a,X4 : a,X3 : a] : ((X0 @ X2 @ (X1 @ X3 @ (X0 @ X2 @ X4))) = (X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4))) <=> ! [X2 : a,X3 : a,X4 : a] : (((X0 @ X2 @ X4) = X4) => ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ X4)))))),
% 1.48/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.38 thf(f1,conjecture,(
% 1.48/1.38 ! [X1 : a > a > a,X0 : a > a > a] : ((! [X2 : a] : ((X1 @ X2 @ X2) = X2) & ! [X2 : a,X3 : a,X4 : a] : ((X0 @ (X0 @ X2 @ X3) @ X4) = (X0 @ X2 @ (X0 @ X3 @ X4))) & ! [X2 : a,X3 : a] : ((X0 @ (X1 @ X2 @ X3) @ X3) = X3) & ! [X4 : a,X3 : a,X2 : a] : ((X1 @ (X1 @ X2 @ X3) @ X4) = (X1 @ X2 @ (X1 @ X3 @ X4))) & ! [X3 : a,X2 : a] : ((X1 @ (X0 @ X2 @ X3) @ X3) = X3) & ! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) = (X0 @ X3 @ X2)) & ! [X2 : a,X3 : a] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)) & ! [X2 : a] : ((X0 @ X2 @ X2) = X2)) => (! [X2 : a,X4 : a,X3 : a] : ((X0 @ X2 @ (X1 @ X3 @ (X0 @ X2 @ X4))) = (X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4))) <=> ! [X2 : a,X3 : a,X4 : a] : (((X0 @ X2 @ X4) = X4) => ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ X4)))))),
% 1.48/1.38 file('/export/starexec/sandbox/tmp/tmp.I5t9o6d3QE/DTF2THF_3622.p',cMODULAR_EQUIV_THM_pme)).
% 1.48/1.38 thf(f531,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : (((sK2 @ (sK3 @ X2 @ X1) @ X1) = X1)) )),
% 1.48/1.38 inference(equality_proxy_clausification,[status(thm)],[f530])).
% 1.48/1.38 thf(f530,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : ((((sK2 @ (sK3 @ X2 @ X1) @ X1) = X1) = $true)) )),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f529])).
% 1.48/1.38 thf(f529,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ (sK3 @ Y0 @ X1) @ X1) = X1)) @ X2))) )),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f528])).
% 1.48/1.38 thf(f528,plain,(
% 1.48/1.38 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ (sK3 @ Y0 @ X1) @ X1) = X1))) = $true)) )),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f527])).
% 1.48/1.38 thf(f527,plain,(
% 1.48/1.38 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))) @ X1) = $true)) )),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f523])).
% 1.48/1.38 thf(f523,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0))))) = $true)),
% 1.48/1.38 inference(boolean_simplification,[status(thm)],[f522])).
% 1.48/1.38 thf(f522,plain,(
% 1.48/1.38 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) = $true)),
% 1.48/1.38 inference(backward_demodulation,[status(thm)],[f57,f521])).
% 1.48/1.38 thf(f521,plain,(
% 1.48/1.38 ($true = (((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) = (sK3 @ Y0 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y0 @ Y1) @ Y2) = (sK3 @ Y0 @ (sK3 @ Y1 @ Y2)))))))))))),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.48/1.38 thf(f57,plain,(
% 1.48/1.38 (((((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) = (sK3 @ Y0 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y0 @ Y1) @ Y2) = (sK3 @ Y0 @ (sK3 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) = $true)),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.48/1.38 thf(f53,plain,(
% 1.48/1.38 ($true = (((((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) = (sK3 @ Y0 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y0 @ Y1) @ Y2) = (sK3 @ Y0 @ (sK3 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))))),
% 1.48/1.38 inference(boolean_simplification,[status(thm)],[f52])).
% 1.48/1.38 thf(f52,plain,(
% 1.48/1.38 ($true = ((((((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) = (sK3 @ Y0 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y0 @ Y1) @ Y2) = (sK3 @ Y0 @ (sK3 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) & $true))),
% 1.48/1.38 inference(backward_demodulation,[status(thm)],[f15,f50])).
% 1.48/1.38 thf(f79,plain,(
% 1.48/1.38 ( ! [X2 : a,X3 : a,X1 : a] : (((sK2 @ (sK2 @ X3 @ X2) @ X1) = (sK2 @ X3 @ (sK2 @ X2 @ X1)))) )),
% 1.48/1.38 inference(equality_proxy_clausification,[status(thm)],[f78])).
% 1.48/1.38 thf(f78,plain,(
% 1.48/1.38 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((sK2 @ (sK2 @ X3 @ X2) @ X1) = (sK2 @ X3 @ (sK2 @ X2 @ X1))))) )),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.48/1.38 thf(f77,plain,(
% 1.48/1.38 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: ((sK2 @ (sK2 @ Y0 @ X2) @ X1) = (sK2 @ Y0 @ (sK2 @ X2 @ X1)))) @ X3) = $true)) )),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f71])).
% 1.48/1.38 thf(f71,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ (sK2 @ Y0 @ X2) @ X1) = (sK2 @ Y0 @ (sK2 @ X2 @ X1))))) = $true)) )),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.48/1.38 thf(f70,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK2 @ Y1 @ Y0) @ X1) = (sK2 @ Y1 @ (sK2 @ Y0 @ X1)))))) @ X2))) )),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f65])).
% 1.48/1.38 thf(f65,plain,(
% 1.48/1.38 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK2 @ Y1 @ Y0) @ X1) = (sK2 @ Y1 @ (sK2 @ Y0 @ X1))))))))) )),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.48/1.38 thf(f64,plain,(
% 1.48/1.38 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))) @ X1))) )),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f59])).
% 1.48/1.38 thf(f59,plain,(
% 1.48/1.38 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))))),
% 1.48/1.38 inference(boolean_simplification,[status(thm)],[f58])).
% 1.48/1.38 thf(f58,plain,(
% 1.48/1.38 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $true)),
% 1.48/1.38 inference(backward_demodulation,[status(thm)],[f53,f57])).
% 1.48/1.38 thf(f517,plain,(
% 1.48/1.38 (((sK2 @ sK9 @ (sK2 @ sK9 @ sK8)) = (sK2 @ sK9 @ sK8)) = $false) | (~spl0_2 | ~spl0_4)),
% 1.48/1.38 inference(not_proxy_clausification,[status(thm)],[f510])).
% 1.48/1.38 thf(f510,plain,(
% 1.48/1.38 ((~ ((sK2 @ sK9 @ (sK2 @ sK9 @ sK8)) = (sK2 @ sK9 @ sK8))) = $true) | (~spl0_2 | ~spl0_4)),
% 1.48/1.38 inference(boolean_simplification,[status(thm)],[f508])).
% 1.48/1.38 thf(f508,plain,(
% 1.48/1.38 ($true = (((sK2 @ sK9 @ (sK2 @ sK9 @ sK8)) = (sK2 @ sK9 @ sK8)) => $false)) | (~spl0_2 | ~spl0_4)),
% 1.48/1.38 inference(superposition,[status(thm)],[f502,f495])).
% 1.48/1.38 thf(f495,plain,(
% 1.48/1.38 (((sK2 @ sK9 @ (sK3 @ sK7 @ (sK2 @ sK9 @ sK8))) = (sK3 @ (sK2 @ sK9 @ sK7) @ (sK2 @ sK9 @ sK8))) = $false) | ~spl0_2),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f494])).
% 1.48/1.38 thf(f494,plain,(
% 1.48/1.38 (((^[Y0 : a]: ((sK2 @ Y0 @ (sK3 @ sK7 @ (sK2 @ Y0 @ sK8))) = (sK3 @ (sK2 @ Y0 @ sK7) @ (sK2 @ Y0 @ sK8)))) @ sK9) = $false) | ~spl0_2),
% 1.48/1.38 inference(sigma_clausification,[status(thm)],[f493])).
% 1.48/1.38 thf(f493,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ (sK3 @ sK7 @ (sK2 @ Y0 @ sK8))) = (sK3 @ (sK2 @ Y0 @ sK7) @ (sK2 @ Y0 @ sK8))))) = $false) | ~spl0_2),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f492])).
% 1.48/1.38 thf(f492,plain,(
% 1.48/1.38 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ (sK3 @ sK7 @ (sK2 @ Y1 @ Y0))) = (sK3 @ (sK2 @ Y1 @ sK7) @ (sK2 @ Y1 @ Y0)))))) @ sK8) = $false) | ~spl0_2),
% 1.48/1.38 inference(sigma_clausification,[status(thm)],[f491])).
% 1.48/1.38 thf(f491,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ (sK3 @ sK7 @ (sK2 @ Y1 @ Y0))) = (sK3 @ (sK2 @ Y1 @ sK7) @ (sK2 @ Y1 @ Y0))))))) = $false) | ~spl0_2),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f490])).
% 1.48/1.38 thf(f490,plain,(
% 1.48/1.38 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1)))))))) @ sK7) = $false) | ~spl0_2),
% 1.48/1.38 inference(sigma_clausification,[status(thm)],[f27])).
% 1.48/1.38 thf(f27,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) = $false) | ~spl0_2),
% 1.48/1.38 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.48/1.38 thf(f26,definition,(
% 1.48/1.38 spl0_2 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) = $false)),
% 1.48/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.48/1.38 thf(f502,plain,(
% 1.48/1.38 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK2 @ X3 @ X1) = X1) => ((sK2 @ X3 @ (sK3 @ X2 @ X1)) = (sK3 @ (sK2 @ X3 @ X2) @ X1))) = $true)) ) | ~spl0_4),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f501])).
% 1.48/1.38 thf(f501,plain,(
% 1.48/1.38 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ Y0 @ X1) = X1) => ((sK2 @ Y0 @ (sK3 @ X2 @ X1)) = (sK3 @ (sK2 @ Y0 @ X2) @ X1)))) @ X3) = $true)) ) | ~spl0_4),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f500])).
% 1.48/1.38 thf(f500,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) = X1) => ((sK2 @ Y0 @ (sK3 @ X2 @ X1)) = (sK3 @ (sK2 @ Y0 @ X2) @ X1))))))) ) | ~spl0_4),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f499])).
% 1.48/1.38 thf(f499,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ X1) = X1) => ((sK2 @ Y1 @ (sK3 @ Y0 @ X1)) = (sK3 @ (sK2 @ Y1 @ Y0) @ X1)))))) @ X2) = $true)) ) | ~spl0_4),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f498])).
% 1.48/1.38 thf(f498,plain,(
% 1.48/1.38 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ X1) = X1) => ((sK2 @ Y1 @ (sK3 @ Y0 @ X1)) = (sK3 @ (sK2 @ Y1 @ Y0) @ X1))))))) = $true)) ) | ~spl0_4),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f497])).
% 1.48/1.38 thf(f497,plain,(
% 1.48/1.38 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0)))))))) @ X1) = $true)) ) | ~spl0_4),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f34])).
% 1.48/1.38 thf(f34,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0))))))))) = $true) | ~spl0_4),
% 1.48/1.38 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.48/1.38 thf(f33,definition,(
% 1.48/1.38 spl0_4 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0))))))))) = $true)),
% 1.48/1.38 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.48/1.38 thf(f486,plain,(
% 1.48/1.38 ~spl0_1),
% 1.48/1.38 inference(avatar_contradiction_clause,[status(thm)],[f485])).
% 1.48/1.38 thf(f485,plain,(
% 1.48/1.38 $false | ~spl0_1),
% 1.48/1.38 inference(trivial_inequality_removal,[status(thm)],[f484])).
% 1.48/1.38 thf(f484,plain,(
% 1.48/1.38 ($true = $false) | ~spl0_1),
% 1.48/1.38 inference(boolean_simplification,[status(thm)],[f483])).
% 1.48/1.38 thf(f483,plain,(
% 1.48/1.38 (((sK2 @ sK6 @ (sK3 @ sK5 @ sK4)) = (sK2 @ sK6 @ (sK3 @ sK5 @ sK4))) = $false) | ~spl0_1),
% 1.48/1.38 inference(backward_demodulation,[status(thm)],[f457,f462])).
% 1.48/1.38 thf(f462,plain,(
% 1.48/1.38 ( ! [X0 : a] : (((sK3 @ (sK2 @ sK6 @ X0) @ sK4) = (sK2 @ sK6 @ (sK3 @ X0 @ sK4)))) ) | ~spl0_1),
% 1.48/1.38 inference(superposition,[status(thm)],[f47,f458])).
% 1.48/1.38 thf(f458,plain,(
% 1.48/1.38 ((sK2 @ sK6 @ sK4) = sK4) | ~spl0_1),
% 1.48/1.38 inference(equality_proxy_clausification,[status(thm)],[f455])).
% 1.48/1.38 thf(f455,plain,(
% 1.48/1.38 (((sK2 @ sK6 @ sK4) = sK4) = $true) | ~spl0_1),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f377])).
% 1.48/1.38 thf(f377,plain,(
% 1.48/1.38 ((((sK2 @ sK6 @ sK4) = sK4) => ((sK2 @ sK6 @ (sK3 @ sK5 @ sK4)) = (sK3 @ (sK2 @ sK6 @ sK5) @ sK4))) = $false) | ~spl0_1),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f376])).
% 1.48/1.38 thf(f376,plain,(
% 1.48/1.38 (((^[Y0 : a]: (((sK2 @ Y0 @ sK4) = sK4) => ((sK2 @ Y0 @ (sK3 @ sK5 @ sK4)) = (sK3 @ (sK2 @ Y0 @ sK5) @ sK4)))) @ sK6) = $false) | ~spl0_1),
% 1.48/1.38 inference(sigma_clausification,[status(thm)],[f323])).
% 1.48/1.38 thf(f323,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK4) = sK4) => ((sK2 @ Y0 @ (sK3 @ sK5 @ sK4)) = (sK3 @ (sK2 @ Y0 @ sK5) @ sK4))))) = $false) | ~spl0_1),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f322])).
% 1.48/1.38 thf(f322,plain,(
% 1.48/1.38 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ sK4) = sK4) => ((sK2 @ Y1 @ (sK3 @ Y0 @ sK4)) = (sK3 @ (sK2 @ Y1 @ Y0) @ sK4)))))) @ sK5) = $false) | ~spl0_1),
% 1.48/1.38 inference(sigma_clausification,[status(thm)],[f265])).
% 1.48/1.38 thf(f265,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ sK4) = sK4) => ((sK2 @ Y1 @ (sK3 @ Y0 @ sK4)) = (sK3 @ (sK2 @ Y1 @ Y0) @ sK4))))))) = $false) | ~spl0_1),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f264])).
% 1.48/1.38 thf(f264,plain,(
% 1.48/1.38 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0)))))))) @ sK4)) | ~spl0_1),
% 1.48/1.38 inference(sigma_clausification,[status(thm)],[f24])).
% 1.48/1.38 thf(f24,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0))))))))) = $false) | ~spl0_1),
% 1.48/1.38 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.48/1.38 thf(f23,definition,(
% 1.48/1.38 spl0_1 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0))))))))) = $false)),
% 1.48/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.48/1.38 thf(f47,plain,(
% 1.48/1.38 ( ! [X2 : a,X3 : a,X1 : a] : (((sK3 @ (sK2 @ X3 @ X1) @ (sK2 @ X3 @ X2)) = (sK2 @ X3 @ (sK3 @ X1 @ (sK2 @ X3 @ X2))))) ) | ~spl0_1),
% 1.48/1.38 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.48/1.38 thf(f46,plain,(
% 1.48/1.38 ( ! [X2 : a,X3 : a,X1 : a] : ((((sK2 @ X3 @ (sK3 @ X1 @ (sK2 @ X3 @ X2))) = (sK3 @ (sK2 @ X3 @ X1) @ (sK2 @ X3 @ X2))) = $true)) ) | ~spl0_1),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.48/1.38 thf(f45,plain,(
% 1.48/1.38 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: ((sK2 @ Y0 @ (sK3 @ X1 @ (sK2 @ Y0 @ X2))) = (sK3 @ (sK2 @ Y0 @ X1) @ (sK2 @ Y0 @ X2)))) @ X3) = $true)) ) | ~spl0_1),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f44])).
% 1.48/1.38 thf(f44,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ (sK3 @ X1 @ (sK2 @ Y0 @ X2))) = (sK3 @ (sK2 @ Y0 @ X1) @ (sK2 @ Y0 @ X2))))) = $true)) ) | ~spl0_1),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.48/1.38 thf(f43,plain,(
% 1.48/1.38 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ (sK3 @ X1 @ (sK2 @ Y1 @ Y0))) = (sK3 @ (sK2 @ Y1 @ X1) @ (sK2 @ Y1 @ Y0)))))) @ X2))) ) | ~spl0_1),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f42])).
% 1.48/1.38 thf(f42,plain,(
% 1.48/1.38 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ (sK3 @ X1 @ (sK2 @ Y1 @ Y0))) = (sK3 @ (sK2 @ Y1 @ X1) @ (sK2 @ Y1 @ Y0))))))))) ) | ~spl0_1),
% 1.48/1.38 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.48/1.38 thf(f41,plain,(
% 1.48/1.38 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1)))))))) @ X1))) ) | ~spl0_1),
% 1.48/1.38 inference(pi_clausification,[status(thm)],[f40])).
% 1.48/1.38 thf(f40,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) != $false) | ~spl0_1),
% 1.48/1.38 inference(forward_demodulation,[status(thm)],[f16,f24])).
% 1.48/1.38 thf(f16,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) != (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0))))))))))),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.48/1.38 thf(f14,plain,(
% 1.48/1.38 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0)))))))))) = $false)),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.48/1.38 thf(f457,plain,(
% 1.48/1.38 (((sK2 @ sK6 @ (sK3 @ sK5 @ sK4)) = (sK3 @ (sK2 @ sK6 @ sK5) @ sK4)) = $false) | ~spl0_1),
% 1.48/1.38 inference(boolean_simplification,[status(thm)],[f456])).
% 1.48/1.38 thf(f456,plain,(
% 1.48/1.38 (($true => ((sK2 @ sK6 @ (sK3 @ sK5 @ sK4)) = (sK3 @ (sK2 @ sK6 @ sK5) @ sK4))) = $false) | ~spl0_1),
% 1.48/1.38 inference(backward_demodulation,[status(thm)],[f377,f455])).
% 1.48/1.38 thf(f39,plain,(
% 1.48/1.38 ~spl0_2 | ~spl0_3),
% 1.48/1.38 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.48/1.38 thf(f38,plain,(
% 1.48/1.38 $false | (~spl0_2 | ~spl0_3)),
% 1.48/1.38 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.48/1.38 thf(f37,plain,(
% 1.48/1.38 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.48/1.38 inference(forward_demodulation,[status(thm)],[f31,f27])).
% 1.48/1.38 thf(f31,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) = $true) | ~spl0_3),
% 1.48/1.38 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.48/1.38 thf(f30,definition,(
% 1.48/1.38 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) = $true)),
% 1.48/1.38 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.48/1.38 thf(f35,plain,(
% 1.48/1.38 spl0_3 | spl0_4),
% 1.48/1.38 inference(avatar_split_clause,[status(thm)],[f20,f33,f30])).
% 1.48/1.38 thf(f20,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) = $true) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0))))))))) = $true)),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.48/1.38 thf(f28,plain,(
% 1.48/1.38 spl0_1 | spl0_2),
% 1.48/1.38 inference(avatar_split_clause,[status(thm)],[f21,f26,f23])).
% 1.48/1.38 thf(f21,plain,(
% 1.48/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) = Y0) => ((sK2 @ Y2 @ (sK3 @ Y1 @ Y0)) = (sK3 @ (sK2 @ Y2 @ Y1) @ Y0))))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ (sK3 @ Y0 @ (sK2 @ Y2 @ Y1))) = (sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1))))))))) = $false)),
% 1.48/1.38 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.48/1.38 % SZS output end Proof for DTF2THF_3622
% 1.48/1.38 % (3775)------------------------------
% 1.48/1.38 % (3775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.38 % (3775)Termination reason: Refutation
% 1.48/1.38
% 1.48/1.38 % (3775)Memory used [KB]: 6524
% 1.48/1.38 % (3775)Time elapsed: 0.101 s
% 1.48/1.38 % (3775)Instructions burned: 315 (million)
% 1.48/1.38 % (3775)------------------------------
% 1.48/1.38 % (3775)------------------------------
% 1.48/1.38 % (3750)Success in time 0.114 s
%------------------------------------------------------------------------------