%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV002^5 : 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 : n024.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 09:40:02 AM UTC 2026
% Result : Theorem 1.62s 1.09s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 1
% Syntax : Number of formulae : 74 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 706 ( 284 equ; 0 cnn)
% Maximal formula atoms : 11 ( 9 avg)
% Number of connectives : 2669 ( 4 ~; 0 |; 152 &;2143 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 6 con; 0-2 aty)
% ( 359 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 525 ( 374 ^; 151 !; 0 ?; 525 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a > a > a ).
thf(func_def_18,type,
sK3: a > a > a ).
thf(func_def_19,type,
sK4: a ).
thf(func_def_20,type,
sK5: a ).
thf(func_def_21,type,
sK6: a ).
thf(f791,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f790]) ).
thf(f790,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f789]) ).
thf(f789,plain,
( ( ( sK3 @ sK5 @ ( sK2 @ sK4 @ sK6 ) )
= ( sK3 @ sK5 @ ( sK2 @ sK4 @ sK6 ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f37,f786]) ).
thf(f786,plain,
! [X2: a,X0: a,X1: a] :
( ( sK3 @ X0 @ ( sK2 @ X2 @ ( sK3 @ X0 @ X1 ) ) )
= ( sK3 @ X0 @ ( sK2 @ X2 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f759,f35]) ).
thf(f35,plain,
! [X2: a,X3: a,X1: a] :
( ( sK2 @ ( sK3 @ X3 @ X2 ) @ ( sK3 @ X3 @ X1 ) )
= ( sK3 @ X3 @ ( sK2 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( sK3 @ X3 @ ( sK2 @ X2 @ X1 ) )
= ( sK2 @ ( sK3 @ X3 @ X2 ) @ ( sK3 @ X3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ ( sK2 @ X2 @ X1 ) )
= ( sK2 @ ( sK3 @ Y0 @ X2 ) @ ( sK3 @ Y0 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ ( sK2 @ X2 @ X1 ) )
= ( sK2 @ ( sK3 @ Y0 @ X2 ) @ ( sK3 @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ ( sK2 @ Y0 @ X1 ) )
= ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ ( sK3 @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ ( sK2 @ Y0 @ X1 ) )
= ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ ( sK3 @ Y1 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ ( sK2 @ Y1 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y2 @ Y1 ) @ ( sK3 @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ ( sK2 @ Y1 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y2 @ Y1 ) @ ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ ( sK2 @ Y1 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y2 @ Y1 ) @ ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f15,f26]) ).
thf(f26,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y0 ) @ Y1 )
= ( sK2 @ Y2 @ ( sK2 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 )
= ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y0 ) @ Y1 )
= ( sK2 @ Y2 @ ( sK2 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 )
= ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ ( sK2 @ Y1 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y2 @ Y1 ) @ ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y0 ) @ Y1 )
= ( sK2 @ Y2 @ ( sK2 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 )
= ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ ( sK2 @ Y1 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y2 @ Y1 ) @ ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ ( sK3 @ Y1 @ Y2 ) )
= ( sK3 @ Y1 @ ( sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > a] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
= ( sK2 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ ( Y0 @ Y1 @ Y3 ) )
= ( Y0 @ ( sK2 @ Y2 @ Y1 ) @ ( sK2 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( Y0 @ Y2 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( sK2 @ Y1 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
= ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ ( sK2 @ Y3 @ Y1 ) @ Y2 )
= ( sK2 @ Y3 @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y1 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ ( sK2 @ Y2 @ Y1 ) )
= ( sK2 @ ( Y0 @ Y3 @ Y2 ) @ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ ( Y0 @ Y2 @ Y1 ) @ ( Y0 @ Y2 @ Y3 ) )
= ( Y0 @ Y2 @ ( sK2 @ Y1 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
= ( sK2 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ ( Y0 @ Y1 @ Y3 ) )
= ( Y0 @ ( sK2 @ Y2 @ Y1 ) @ ( sK2 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( Y0 @ Y2 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( sK2 @ Y1 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
= ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ ( sK2 @ Y3 @ Y1 ) @ Y2 )
= ( sK2 @ Y3 @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y1 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ ( sK2 @ Y2 @ Y1 ) )
= ( sK2 @ ( Y0 @ Y3 @ Y2 ) @ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ ( Y0 @ Y2 @ Y1 ) @ ( Y0 @ Y2 @ Y3 ) )
= ( Y0 @ Y2 @ ( sK2 @ Y1 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $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] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
= ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ ( Y1 @ Y2 @ Y4 ) )
= ( Y1 @ ( Y0 @ Y3 @ Y2 ) @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y2 @ Y3 ) @ Y3 )
= Y3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
= ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y0 @ Y4 @ Y2 ) @ Y3 )
= ( Y0 @ Y4 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ Y3 @ ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y1 @ Y4 @ Y3 ) @ ( Y1 @ Y4 @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ ( Y1 @ Y3 @ Y4 ) )
= ( Y1 @ Y3 @ ( Y0 @ Y2 @ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
@ 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] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
= ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ ( Y1 @ Y2 @ Y4 ) )
= ( Y1 @ ( Y0 @ Y3 @ Y2 ) @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y2 @ Y3 ) @ Y3 )
= Y3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
= ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y0 @ Y4 @ Y2 ) @ Y3 )
= ( Y0 @ Y4 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ Y3 @ ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y1 @ Y4 @ Y3 ) @ ( Y1 @ Y4 @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ ( Y1 @ Y3 @ Y4 ) )
= ( Y1 @ Y3 @ ( Y0 @ Y2 @ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
= $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] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
= ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ ( Y1 @ Y2 @ Y4 ) )
= ( Y1 @ ( Y0 @ Y3 @ Y2 ) @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y2 @ Y3 ) @ Y3 )
= Y3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
= ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y0 @ Y4 @ Y2 ) @ Y3 )
= ( Y0 @ Y4 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ Y3 @ ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y1 @ Y4 @ Y3 ) @ ( Y1 @ Y4 @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ ( Y1 @ Y3 @ Y4 ) )
= ( Y1 @ Y3 @ ( Y0 @ Y2 @ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $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] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
= ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ ( Y1 @ Y2 @ Y4 ) )
= ( Y1 @ ( Y0 @ Y3 @ Y2 ) @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y2 @ Y3 ) @ Y3 )
= Y3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
= ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y0 @ Y4 @ Y2 ) @ Y3 )
= ( Y0 @ Y4 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ Y3 @ ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y1 @ Y4 @ Y3 ) @ ( Y1 @ Y4 @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ ( Y1 @ Y3 @ Y4 ) )
= ( Y1 @ Y3 @ ( Y0 @ Y2 @ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a,X4: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) )
& ! [X5: a,X6: a,X7: a] :
( ( X0 @ ( X0 @ X6 @ X5 ) @ X7 )
= ( X0 @ X6 @ ( X0 @ X5 @ X7 ) ) )
& ! [X8: a,X9: a,X10: a] :
( ( X1 @ ( X1 @ X8 @ X10 ) @ X9 )
= ( X1 @ X8 @ ( X1 @ X10 @ X9 ) ) )
& ! [X11: a,X12: a] :
( ( X0 @ X12 @ X11 )
= ( X0 @ X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( X0 @ ( X1 @ X14 @ X13 ) @ X13 )
= X13 )
& ! [X15: a] :
( ( X0 @ X15 @ X15 )
= X15 )
& ! [X16: a,X17: a] :
( ( X1 @ ( X0 @ X16 @ X17 ) @ X17 )
= X17 )
& ! [X18: a] :
( ( X1 @ X18 @ X18 )
= X18 )
& ! [X19: a,X20: a,X21: a] :
( ( X1 @ X20 @ ( X0 @ X21 @ X19 ) )
= ( X0 @ ( X1 @ X20 @ X21 ) @ ( X1 @ X20 @ X19 ) ) )
& ! [X22: a,X23: a] :
( ( X1 @ X22 @ X23 )
= ( X1 @ X23 @ X22 ) ) )
=> ! [X24: a,X25: a,X26: a] :
( ( X1 @ ( X0 @ X25 @ X26 ) @ ( X0 @ X25 @ X24 ) )
= ( X0 @ X25 @ ( X1 @ X26 @ ( X0 @ X25 @ X24 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a,X4: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) )
& ! [X3: a,X2: a,X4: a] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) )
& ! [X2: a,X4: a,X3: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X0 @ X3 @ X2 ) )
& ! [X3: a,X2: a] :
( ( X0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 )
& ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 )
& ! [X4: a,X2: a,X3: a] :
( ( X1 @ X2 @ ( X0 @ X3 @ X4 ) )
= ( X0 @ ( X1 @ X2 @ X3 ) @ ( X1 @ X2 @ X4 ) ) )
& ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) ) )
=> ! [X4: a,X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) )
= ( X0 @ X2 @ ( X1 @ X3 @ ( X0 @ X2 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a,X4: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) )
& ! [X3: a,X2: a,X4: a] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) )
& ! [X2: a,X4: a,X3: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X0 @ X3 @ X2 ) )
& ! [X3: a,X2: a] :
( ( X0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 )
& ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 )
& ! [X4: a,X2: a,X3: a] :
( ( X1 @ X2 @ ( X0 @ X3 @ X4 ) )
= ( X0 @ ( X1 @ X2 @ X3 ) @ ( X1 @ X2 @ X4 ) ) )
& ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) ) )
=> ! [X4: a,X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) )
= ( X0 @ X2 @ ( X1 @ X3 @ ( X0 @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q33ztibo3p/DTF2THF_25816.p',cMODULAR_THM_DEF2_pme) ).
thf(f759,plain,
! [X2: a,X0: a,X1: a] :
( ( sK3 @ X0 @ ( sK2 @ X2 @ ( sK3 @ X0 @ X1 ) ) )
= ( sK2 @ ( sK3 @ X0 @ X2 ) @ ( sK3 @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f35,f345]) ).
thf(f345,plain,
! [X0: a,X1: a] :
( ( sK3 @ X0 @ ( sK3 @ X0 @ X1 ) )
= ( sK3 @ X0 @ X1 ) ),
inference(superposition,[status(thm)],[f276,f204]) ).
thf(f204,plain,
! [X0: a] :
( ( sK3 @ X0 @ X0 )
= X0 ),
inference(forward_demodulation,[status(thm)],[f189,f81]) ).
thf(f81,plain,
! [X2: a,X1: a] :
( ( sK3 @ X2 @ ( sK2 @ X1 @ X2 ) )
= X2 ),
inference(equality_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: a,X1: a] :
( ( ( sK3 @ X2 @ ( sK2 @ X1 @ X2 ) )
= X2 )
= $true ),
inference(forward_demodulation,[status(thm)],[f67,f65]) ).
thf(f65,plain,
! [X2: a,X1: a] :
( ( sK3 @ X1 @ X2 )
= ( sK3 @ X2 @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
= ( sK3 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
= ( sK3 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
= ( sK3 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f44,f45]) ).
thf(f45,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y0 ) @ Y1 )
= ( sK2 @ Y2 @ ( sK2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y0 ) @ Y1 )
= ( sK2 @ Y2 @ ( sK2 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK2 @ Y2 @ Y0 ) @ Y1 )
= ( sK2 @ Y2 @ ( sK2 @ Y0 @ Y1 ) ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f26,f41]) ).
thf(f41,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 )
= ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f67,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK3 @ ( sK2 @ X1 @ X2 ) @ X2 )
= X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ ( sK2 @ X1 @ Y0 ) @ Y0 )
= Y0 )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ ( sK2 @ X1 @ Y0 ) @ Y0 )
= Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f59]) ).
thf(f59,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f54,f58]) ).
thf(f58,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK3 @ Y0 @ Y2 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ Y1 )
= Y1 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f48,f51]) ).
thf(f189,plain,
! [X0: a,X1: a] :
( ( sK3 @ X0 @ ( sK3 @ X0 @ ( sK2 @ X1 @ X0 ) ) )
= X0 ),
inference(superposition,[status(thm)],[f181,f35]) ).
thf(f181,plain,
! [X0: a,X1: a] :
( ( sK3 @ X0 @ ( sK2 @ X1 @ ( sK3 @ X0 @ X0 ) ) )
= X0 ),
inference(forward_demodulation,[status(thm)],[f180,f81]) ).
thf(f180,plain,
! [X0: a,X1: a] :
( ( sK3 @ X0 @ ( sK2 @ X1 @ ( sK3 @ X0 @ X0 ) ) )
= ( sK3 @ X0 @ ( sK2 @ X1 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f172,f35]) ).
thf(f172,plain,
! [X0: a,X1: a] :
( ( sK3 @ X0 @ ( sK2 @ X1 @ ( sK3 @ X0 @ X0 ) ) )
= ( sK2 @ ( sK3 @ X0 @ X1 ) @ ( sK3 @ X0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f35,f125]) ).
thf(f125,plain,
! [X0: a] :
( ( sK3 @ X0 @ X0 )
= ( sK3 @ X0 @ ( sK3 @ X0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f65,f99]) ).
thf(f99,plain,
! [X0: a] :
( ( sK3 @ X0 @ X0 )
= ( sK3 @ ( sK3 @ X0 @ X0 ) @ X0 ) ),
inference(superposition,[status(thm)],[f85,f81]) ).
thf(f85,plain,
! [X2: a,X0: a,X1: a] :
( ( sK3 @ X0 @ X2 )
= ( sK3 @ ( sK3 @ X0 @ X2 ) @ ( sK3 @ X0 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f81,f35]) ).
thf(f276,plain,
! [X2: a,X3: a,X1: a] :
( ( sK3 @ X2 @ ( sK3 @ X3 @ X1 ) )
= ( sK3 @ ( sK3 @ X2 @ X3 ) @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f263]) ).
thf(f263,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( sK3 @ ( sK3 @ X2 @ X3 ) @ X1 )
= ( sK3 @ X2 @ ( sK3 @ X3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f262]) ).
thf(f262,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ ( sK3 @ X2 @ Y0 ) @ X1 )
= ( sK3 @ X2 @ ( sK3 @ Y0 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f188]) ).
thf(f188,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ ( sK3 @ X2 @ Y0 ) @ X1 )
= ( sK3 @ X2 @ ( sK3 @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f187]) ).
thf(f187,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK3 @ Y0 @ Y1 ) @ X1 )
= ( sK3 @ Y0 @ ( sK3 @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK3 @ Y0 @ Y1 ) @ X1 )
= ( sK3 @ Y0 @ ( sK3 @ Y1 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 )
= ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f37,plain,
( ( ( sK3 @ sK5 @ ( sK2 @ sK4 @ sK6 ) )
= ( sK3 @ sK5 @ ( sK2 @ sK4 @ ( sK3 @ sK5 @ sK6 ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f23,f35]) ).
thf(f23,plain,
( ( ( sK2 @ ( sK3 @ sK5 @ sK4 ) @ ( sK3 @ sK5 @ sK6 ) )
= ( sK3 @ sK5 @ ( sK2 @ sK4 @ ( sK3 @ sK5 @ sK6 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a] :
( ( sK2 @ ( sK3 @ sK5 @ sK4 ) @ ( sK3 @ sK5 @ Y0 ) )
= ( sK3 @ sK5 @ ( sK2 @ sK4 @ ( sK3 @ sK5 @ Y0 ) ) ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ ( sK3 @ sK5 @ sK4 ) @ ( sK3 @ sK5 @ Y0 ) )
= ( sK3 @ sK5 @ ( sK2 @ sK4 @ ( sK3 @ sK5 @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y0 @ sK4 ) @ ( sK3 @ Y0 @ Y1 ) )
= ( sK3 @ Y0 @ ( sK2 @ sK4 @ ( sK3 @ Y0 @ Y1 ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y0 @ sK4 ) @ ( sK3 @ Y0 @ Y1 ) )
= ( sK3 @ Y0 @ ( sK2 @ sK4 @ ( sK3 @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ ( sK3 @ Y1 @ Y2 ) )
= ( sK3 @ Y1 @ ( sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ ( sK3 @ Y1 @ Y2 ) )
= ( sK3 @ Y1 @ ( sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ ( sK3 @ Y1 @ Y2 ) )
= ( sK3 @ Y1 @ ( sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f13,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV002^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:37:40 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEV002^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Set Theory (Relations)
% 0.07/0.32 % Problem : TPS problem from LATTICES-THMS
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_1180 [Bro09]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % 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, 0.12 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.07/0.32 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.07/0.32 % Number of atoms : 11 ( 11 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 11 ( 11 avg)
% 0.07/0.32 % Number of connectives : 78 ( 0 ~; 0 |; 9 &; 68 @)
% 0.07/0.32 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 16 ( 16 avg)
% 0.07/0.32 % Number of types : 1 ( 1 usr)
% 0.07/0.32 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.07/0.32 % Number of variables : 27 ( 0 ^; 27 !; 0 ?; 27 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(a_type,type,
% 0.07/0.32 a: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(cMODULAR_THM_DEF2_pme,conjecture,
% 0.07/0.32 ! [JOIN: a > a > a,MEET: a > a > a] :
% 0.07/0.32 ( ( ! [Xx: a] :
% 0.07/0.32 ( ( JOIN @ Xx @ Xx )
% 0.07/0.32 = Xx )
% 0.07/0.32 & ! [Xx: a] :
% 0.07/0.32 ( ( MEET @ Xx @ Xx )
% 0.07/0.32 = Xx )
% 0.07/0.32 & ! [Xx: a,Xy: a,Xz: a] :
% 0.07/0.32 ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
% 0.07/0.32 = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
% 0.07/0.32 & ! [Xx: a,Xy: a,Xz: a] :
% 0.07/0.32 ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
% 0.07/0.32 = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
% 0.07/0.32 & ! [Xx: a,Xy: a] :
% 0.07/0.32 ( ( JOIN @ Xx @ Xy )
% 0.07/0.32 = ( JOIN @ Xy @ Xx ) )
% 0.07/0.32 & ! [Xx: a,Xy: a] :
% 0.07/0.32 ( ( MEET @ Xx @ Xy )
% 0.07/0.32 = ( MEET @ Xy @ Xx ) )
% 0.07/0.32 & ! [Xx: a,Xy: a] :
% 0.07/0.32 ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
% 0.07/0.32 = Xy )
% 0.07/0.32 & ! [Xx: a,Xy: a] :
% 0.07/0.32 ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
% 0.07/0.32 = Xy )
% 0.07/0.32 & ! [Xx: a,Xy: a,Xz: a] :
% 0.07/0.32 ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 0.07/0.32 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
% 0.07/0.32 & ! [Xx: a,Xy: a,Xz: a] :
% 0.07/0.32 ( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
% 0.07/0.32 = ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) )
% 0.07/0.32 => ! [Xx: a,Xy: a,Xz: a] :
% 0.07/0.32 ( ( JOIN @ Xx @ ( MEET @ Xy @ ( JOIN @ Xx @ Xz ) ) )
% 0.07/0.32 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.04/0.91 ---- Embedded in THF ---
% 1.04/0.91 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.04/0.91 %%% Generated on Tue Feb 24 07:37:41 EST 2026
% 1.04/0.91 %%% using '$$dhol' embedding, version 1.3.0.
% 1.04/0.91 %%% Logic specification used:
% 1.04/0.91 %%% thf(spec, logic, $$dhol).
% 1.04/0.91
% 1.04/0.91 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Q33ztibo3p/DTF2DTF25816.p
% See solution above
% 1.04/0.91 ------------------------
% 1.04/0.92 ---- Cleaned THF ---
% 1.04/0.92 thf(a_type,type,
% 1.04/0.92 a: $tType ).
% 1.04/0.92
% 1.04/0.92 thf(cMODULAR_THM_DEF2_pme,conjecture,
% 1.04/0.92 ! [JOIN: a > a > a,MEET: a > a > a] :
% 1.04/0.92 ( ( ! [Xx: a] :
% 1.04/0.92 ( ( JOIN @ Xx @ Xx )
% 1.04/0.92 = Xx )
% 1.04/0.92 & ! [Xx: a] :
% 1.04/0.92 ( ( MEET @ Xx @ Xx )
% 1.04/0.92 = Xx )
% 1.04/0.92 & ! [Xx: a,Xy: a,Xz: a] :
% 1.04/0.92 ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
% 1.04/0.92 = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
% 1.04/0.92 & ! [Xx: a,Xy: a,Xz: a] :
% 1.04/0.92 ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
% 1.04/0.92 = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
% 1.04/0.92 & ! [Xx: a,Xy: a] :
% 1.04/0.92 ( ( JOIN @ Xx @ Xy )
% 1.04/0.92 = ( JOIN @ Xy @ Xx ) )
% 1.04/0.92 & ! [Xx: a,Xy: a] :
% 1.04/0.92 ( ( MEET @ Xx @ Xy )
% 1.04/0.92 = ( MEET @ Xy @ Xx ) )
% 1.04/0.92 & ! [Xx: a,Xy: a] :
% 1.04/0.92 ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
% 1.04/0.92 = Xy )
% 1.04/0.92 & ! [Xx: a,Xy: a] :
% 1.04/0.92 ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
% 1.04/0.92 = Xy )
% 1.04/0.92 & ! [Xx: a,Xy: a,Xz: a] :
% 1.04/0.92 ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 1.04/0.92 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
% 1.04/0.92 & ! [Xx: a,Xy: a,Xz: a] :
% 1.04/0.92 ( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
% 1.04/0.92 = ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) )
% 1.04/0.92 => ! [Xx: a,Xy: a,Xz: a] :
% 1.04/0.92 ( ( JOIN @ Xx @ ( MEET @ Xy @ ( JOIN @ Xx @ Xz ) ) )
% 1.04/0.92 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) ) ) ).
% 1.04/0.92 ------------------------
% 1.04/0.93 % (26009)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_25816 for (3000ds/2Mi)
% 1.04/0.93 % (26007)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_25816 for (3000ds/27Mi)
% 1.04/0.93 % (26008)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25816 for (3000ds/2Mi)
% 1.04/0.93 % (26006)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_25816 for (3000ds/4Mi)
% 1.04/0.93 % (26005)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25816 for (3000ds/183Mi)
% 1.04/0.93 % (26011)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25816 for (3000ds/18Mi)
% 1.04/0.93 % (26010)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_25816 for (3000ds/275Mi)
% 1.04/0.93 % (26008)Instruction limit reached!
% 1.04/0.93 % (26008)------------------------------
% 1.04/0.93 % (26008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.93 % (26008)Termination reason: Unknown
% 1.04/0.93 % (26008)Termination phase: Saturation
% 1.04/0.93
% 1.04/0.93 % (26008)Memory used [KB]: 1023
% 1.04/0.93 % (26008)Time elapsed: 0.002 s
% 1.04/0.93 % (26008)Instructions burned: 3 (million)
% 1.04/0.93 % (26008)------------------------------
% 1.04/0.93 % (26008)------------------------------
% 1.04/0.93 % (26009)Instruction limit reached!
% 1.04/0.93 % (26009)------------------------------
% 1.04/0.93 % (26009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.93 % (26009)Termination reason: Unknown
% 1.04/0.93 % (26009)Termination phase: Property scanning
% 1.04/0.93
% 1.04/0.93 % (26009)Memory used [KB]: 1023
% 1.04/0.93 % (26009)Time elapsed: 0.002 s
% 1.04/0.93 % (26009)Instructions burned: 3 (million)
% 1.04/0.93 % (26009)------------------------------
% 1.04/0.93 % (26009)------------------------------
% 1.04/0.93 % (26006)Instruction limit reached!
% 1.04/0.93 % (26006)------------------------------
% 1.04/0.93 % (26006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.93 % (26006)Termination reason: Unknown
% 1.04/0.93 % (26006)Termination phase: Saturation
% 1.04/0.93
% 1.04/0.93 % (26006)Memory used [KB]: 5500
% 1.04/0.93 % (26006)Time elapsed: 0.003 s
% 1.04/0.93 % (26006)Instructions burned: 5 (million)
% 1.04/0.93 % (26006)------------------------------
% 1.04/0.93 % (26006)------------------------------
% 1.04/0.94 % (26011)Instruction limit reached!
% 1.04/0.94 % (26011)------------------------------
% 1.04/0.94 % (26011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.94 % (26011)Termination reason: Unknown
% 1.04/0.94 % (26011)Termination phase: Saturation
% 1.04/0.94
% 1.04/0.94 % (26011)Memory used [KB]: 5628
% 1.04/0.94 % (26011)Time elapsed: 0.007 s
% 1.04/0.94 % (26011)Instructions burned: 18 (million)
% 1.04/0.94 % (26011)------------------------------
% 1.04/0.94 % (26011)------------------------------
% 1.04/0.94 % (26007)Instruction limit reached!
% 1.04/0.94 % (26007)------------------------------
% 1.04/0.94 % (26007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.94 % (26007)Termination reason: Unknown
% 1.04/0.94 % (26007)Termination phase: Saturation
% 1.04/0.94
% 1.04/0.94 % (26007)Memory used [KB]: 5628
% 1.04/0.94 % (26007)Time elapsed: 0.010 s
% 1.04/0.94 % (26007)Instructions burned: 28 (million)
% 1.04/0.94 % (26007)------------------------------
% 1.04/0.94 % (26007)------------------------------
% 1.04/0.94 % (26012)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/3Mi)
% 1.04/0.94 % (26014)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_25816 for (2999ds/15Mi)
% 1.04/0.94 % (26012)Instruction limit reached!
% 1.04/0.94 % (26012)------------------------------
% 1.04/0.94 % (26012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.94 % (26012)Termination reason: Unknown
% 1.04/0.94 % (26012)Termination phase: Saturation
% 1.04/0.94
% 1.04/0.94 % (26012)Memory used [KB]: 5500
% 1.04/0.94 % (26012)Time elapsed: 0.003 s
% 1.04/0.94 % (26012)Instructions burned: 5 (million)
% 1.04/0.94 % (26012)------------------------------
% 1.04/0.94 % (26012)------------------------------
% 1.04/0.94 % (26013)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_25816 for (2999ds/37Mi)
% 1.04/0.95 % (26015)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_25816 for (2999ds/3Mi)
% 1.04/0.95 % (26014)Instruction limit reached!
% 1.04/0.95 % (26014)------------------------------
% 1.04/0.95 % (26014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.95 % (26014)Termination reason: Unknown
% 1.04/0.95 % (26014)Termination phase: Saturation
% 1.04/0.95
% 1.04/0.95 % (26014)Memory used [KB]: 5628
% 1.04/0.95 % (26014)Time elapsed: 0.006 s
% 1.04/0.95 % (26014)Instructions burned: 15 (million)
% 1.04/0.95 % (26014)------------------------------
% 1.04/0.95 % (26014)------------------------------
% 1.04/0.95 % (26015)Instruction limit reached!
% 1.04/0.95 % (26015)------------------------------
% 1.04/0.95 % (26015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.95 % (26015)Termination reason: Unknown
% 1.04/0.95 % (26015)Termination phase: Saturation
% 1.04/0.95
% 1.04/0.95 % (26015)Memory used [KB]: 1023
% 1.04/0.95 % (26015)Time elapsed: 0.002 s
% 1.04/0.95 % (26015)Instructions burned: 3 (million)
% 1.04/0.95 % (26015)------------------------------
% 1.04/0.95 % (26015)------------------------------
% 1.04/0.95 % (26019)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_25816 for (2999ds/1041Mi)
% 1.04/0.95 % (26022)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/7Mi)
% 1.04/0.96 % (26013)Instruction limit reached!
% 1.04/0.96 % (26013)------------------------------
% 1.04/0.96 % (26013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.96 % (26013)Termination reason: Unknown
% 1.04/0.96 % (26013)Termination phase: Saturation
% 1.04/0.96
% 1.04/0.96 % (26013)Memory used [KB]: 5756
% 1.04/0.96 % (26013)Time elapsed: 0.014 s
% 1.04/0.96 % (26013)Instructions burned: 37 (million)
% 1.04/0.96 % (26013)------------------------------
% 1.04/0.96 % (26013)------------------------------
% 1.04/0.96 % (26025)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_25816 for (2999ds/3Mi)
% 1.04/0.96 % (26022)Instruction limit reached!
% 1.04/0.96 % (26022)------------------------------
% 1.04/0.96 % (26022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.96 % (26022)Termination reason: Unknown
% 1.04/0.96 % (26022)Termination phase: Saturation
% 1.04/0.96 % (26025)Instruction limit reached!
% 1.04/0.96 % (26025)------------------------------
% 1.04/0.96 % (26025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.96 % (26025)Termination reason: Unknown
% 1.04/0.96 % (26025)Termination phase: Twee Goal Transformation
% 1.04/0.96
% 1.04/0.96 % (26025)Memory used [KB]: 1023
% 1.04/0.96 % (26025)Time elapsed: 0.002 s
% 1.04/0.96 % (26025)Instructions burned: 4 (million)
% 1.04/0.96 % (26025)------------------------------
% 1.04/0.96 % (26025)------------------------------
% 1.04/0.96
% 1.04/0.96 % (26022)Memory used [KB]: 1023
% 1.04/0.96 % (26022)Time elapsed: 0.006 s
% 1.04/0.96 % (26022)Instructions burned: 8 (million)
% 1.04/0.96 % (26022)------------------------------
% 1.04/0.96 % (26022)------------------------------
% 1.04/0.96 % (26024)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/16Mi)
% 1.04/0.97 % (26035)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/7Mi)
% 1.04/0.97 % (26024)Instruction limit reached!
% 1.04/0.97 % (26024)------------------------------
% 1.04/0.97 % (26024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.97 % (26024)Termination reason: Unknown
% 1.04/0.97 % (26024)Termination phase: Saturation
% 1.04/0.97
% 1.04/0.97 % (26024)Memory used [KB]: 5628
% 1.04/0.97 % (26024)Time elapsed: 0.010 s
% 1.04/0.97 % (26024)Instructions burned: 16 (million)
% 1.04/0.97 % (26024)------------------------------
% 1.04/0.97 % (26024)------------------------------
% 1.04/0.97 % (26035)Refutation not found, incomplete strategy
% 1.04/0.97 % (26035)------------------------------
% 1.04/0.97 % (26035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.97 % (26035)Termination reason: Refutation not found, incomplete strategy
% 1.04/0.97
% 1.04/0.97
% 1.04/0.97 % (26035)Memory used [KB]: 5500
% 1.04/0.97 % (26035)Time elapsed: 0.003 s
% 1.04/0.97 % (26035)Instructions burned: 6 (million)
% 1.04/0.97 % (26035)------------------------------
% 1.04/0.97 % (26035)------------------------------
% 1.04/0.97 % (26036)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/3Mi)
% 1.04/0.97 % (26034)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_25816 for (2999ds/3Mi)
% 1.04/0.97 % (26036)Instruction limit reached!
% 1.04/0.97 % (26036)------------------------------
% 1.04/0.97 % (26036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.97 % (26036)Termination reason: Unknown
% 1.04/0.97 % (26036)Termination phase: Saturation
% 1.04/0.97
% 1.04/0.97 % (26036)Memory used [KB]: 1023
% 1.04/0.97 % (26036)Time elapsed: 0.002 s
% 1.04/0.97 % (26036)Instructions burned: 4 (million)
% 1.04/0.97 % (26036)------------------------------
% 1.04/0.97 % (26036)------------------------------
% 1.04/0.98 % (26034)Instruction limit reached!
% 1.04/0.98 % (26034)------------------------------
% 1.04/0.98 % (26034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.98 % (26034)Termination reason: Unknown
% 1.04/0.98 % (26034)Termination phase: Property scanning
% 1.04/0.98
% 1.04/0.98 % (26034)Memory used [KB]: 1023
% 1.04/0.98 % (26034)Time elapsed: 0.003 s
% 1.04/0.98 % (26034)Instructions burned: 4 (million)
% 1.04/0.98 % (26034)------------------------------
% 1.04/0.98 % (26034)------------------------------
% 1.04/0.98 % (26042)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/710Mi)
% 1.04/0.98 % (26039)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/4Mi)
% 1.04/0.99 % (26039)Instruction limit reached!
% 1.04/0.99 % (26039)------------------------------
% 1.04/0.99 % (26039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.99 % (26039)Termination reason: Unknown
% 1.04/0.99 % (26039)Termination phase: Saturation
% 1.04/0.99
% 1.04/0.99 % (26039)Memory used [KB]: 5500
% 1.04/0.99 % (26039)Time elapsed: 0.003 s
% 1.04/0.99 % (26039)Instructions burned: 5 (million)
% 1.04/0.99 % (26039)------------------------------
% 1.04/0.99 % (26039)------------------------------
% 1.04/0.99 % (26040)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/18Mi)
% 1.04/0.99 % (26043)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/6Mi)
% 1.04/0.99 % (26043)Instruction limit reached!
% 1.04/0.99 % (26043)------------------------------
% 1.04/0.99 % (26043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.99 % (26043)Termination reason: Unknown
% 1.04/0.99 % (26043)Termination phase: Saturation
% 1.04/0.99
% 1.04/0.99 % (26043)Memory used [KB]: 5500
% 1.04/0.99 % (26043)Time elapsed: 0.005 s
% 1.04/0.99 % (26043)Instructions burned: 7 (million)
% 1.04/0.99 % (26043)------------------------------
% 1.04/0.99 % (26043)------------------------------
% 1.04/1.00 % (26040)Instruction limit reached!
% 1.04/1.00 % (26040)------------------------------
% 1.04/1.00 % (26040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/1.00 % (26040)Termination reason: Unknown
% 1.04/1.00 % (26040)Termination phase: Saturation
% 1.04/1.00
% 1.04/1.00 % (26040)Memory used [KB]: 5628
% 1.04/1.00 % (26040)Time elapsed: 0.010 s
% 1.04/1.00 % (26040)Instructions burned: 18 (million)
% 1.04/1.00 % (26040)------------------------------
% 1.04/1.00 % (26040)------------------------------
% 1.04/1.00 % (26046)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_25816 for (2999ds/902Mi)
% 1.04/1.01 % (26005)Instruction limit reached!
% 1.04/1.01 % (26005)------------------------------
% 1.04/1.01 % (26005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/1.01 % (26005)Termination reason: Unknown
% 1.04/1.01 % (26005)Termination phase: Saturation
% 1.04/1.01
% 1.04/1.01 % (26005)Memory used [KB]: 6524
% 1.04/1.01 % (26005)Time elapsed: 0.078 s
% 1.04/1.01 % (26005)Instructions burned: 183 (million)
% 1.04/1.01 % (26005)------------------------------
% 1.04/1.01 % (26005)------------------------------
% 1.04/1.01 % (26048)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_25816 for (2999ds/21Mi)
% 1.04/1.01 % (26051)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/5Mi)
% 1.04/1.01 % (26051)Instruction limit reached!
% 1.04/1.01 % (26051)------------------------------
% 1.04/1.01 % (26051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/1.01 % (26051)Termination reason: Unknown
% 1.04/1.01 % (26051)Termination phase: Saturation
% 1.04/1.01
% 1.04/1.01 % (26051)Memory used [KB]: 5500
% 1.04/1.01 % (26051)Time elapsed: 0.004 s
% 1.04/1.01 % (26051)Instructions burned: 6 (million)
% 1.04/1.01 % (26051)------------------------------
% 1.04/1.01 % (26051)------------------------------
% 1.62/1.02 % (26048)Instruction limit reached!
% 1.62/1.02 % (26048)------------------------------
% 1.62/1.02 % (26048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.02 % (26048)Termination reason: Unknown
% 1.62/1.02 % (26048)Termination phase: Saturation
% 1.62/1.02
% 1.62/1.02 % (26048)Memory used [KB]: 5628
% 1.62/1.02 % (26048)Time elapsed: 0.013 s
% 1.62/1.02 % (26048)Instructions burned: 22 (million)
% 1.62/1.02 % (26048)------------------------------
% 1.62/1.02 % (26048)------------------------------
% 1.62/1.02 % (26054)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_25816 for (2999ds/6Mi)
% 1.62/1.03 % (26054)Instruction limit reached!
% 1.62/1.03 % (26054)------------------------------
% 1.62/1.03 % (26054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.03 % (26054)Termination reason: Unknown
% 1.62/1.03 % (26054)Termination phase: Saturation
% 1.62/1.03
% 1.62/1.03 % (26054)Memory used [KB]: 5500
% 1.62/1.03 % (26054)Time elapsed: 0.005 s
% 1.62/1.03 % (26054)Instructions burned: 7 (million)
% 1.62/1.03 % (26054)------------------------------
% 1.62/1.03 % (26054)------------------------------
% 1.62/1.03 % (26057)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25816 for (2999ds/377Mi)
% 1.62/1.04 % (26059)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_25816 for (2999ds/779Mi)
% 1.62/1.04 % (26062)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_25816 for (2999ds/19Mi)
% 1.62/1.05 % (26062)Instruction limit reached!
% 1.62/1.05 % (26062)------------------------------
% 1.62/1.05 % (26062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.05 % (26062)Termination reason: Unknown
% 1.62/1.05 % (26062)Termination phase: Saturation
% 1.62/1.05
% 1.62/1.05 % (26062)Memory used [KB]: 5628
% 1.62/1.05 % (26062)Time elapsed: 0.010 s
% 1.62/1.05 % (26062)Instructions burned: 20 (million)
% 1.62/1.05 % (26062)------------------------------
% 1.62/1.05 % (26062)------------------------------
% 1.62/1.06 % (26010)Instruction limit reached!
% 1.62/1.06 % (26010)------------------------------
% 1.62/1.06 % (26010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.06 % (26010)Termination reason: Unknown
% 1.62/1.06 % (26010)Termination phase: Saturation
% 1.62/1.06
% 1.62/1.06 % (26010)Memory used [KB]: 6012
% 1.62/1.06 % (26010)Time elapsed: 0.116 s
% 1.62/1.06 % (26010)Instructions burned: 276 (million)
% 1.62/1.06 % (26010)------------------------------
% 1.62/1.06 % (26010)------------------------------
% 1.62/1.07 % (26067)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25816 for (2998ds/879Mi)
% 1.62/1.08 % (26069)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25816 for (2998ds/17Mi)
% 1.62/1.09 % (26019)First to succeed.
% 1.62/1.09 % (26069)Instruction limit reached!
% 1.62/1.09 % (26069)------------------------------
% 1.62/1.09 % (26069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.09 % (26069)Termination reason: Unknown
% 1.62/1.09 % (26069)Termination phase: Saturation
% 1.62/1.09
% 1.62/1.09 % (26069)Memory used [KB]: 5500
% 1.62/1.09 % (26069)Time elapsed: 0.010 s
% 1.62/1.09 % (26069)Instructions burned: 17 (million)
% 1.62/1.09 % (26069)------------------------------
% 1.62/1.09 % (26069)------------------------------
% 1.62/1.09 % (26019)Refutation found. Thanks to Tanya!
% 1.62/1.09 % SZS status Theorem for DTF2THF_25816
% 1.62/1.09 % SZS output start Proof for DTF2THF_25816
% 1.62/1.09 thf(type_def_5, type, a: $tType).
% 1.62/1.09 thf(func_def_0, type, a: $tType).
% 1.62/1.09 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.62/1.09 thf(func_def_17, type, sK2: a > a > a).
% 1.62/1.09 thf(func_def_18, type, sK3: a > a > a).
% 1.62/1.09 thf(func_def_19, type, sK4: a).
% 1.62/1.09 thf(func_def_20, type, sK5: a).
% 1.62/1.09 thf(func_def_21, type, sK6: a).
% 1.62/1.09 thf(f791,plain,(
% 1.62/1.09 $false),
% 1.62/1.09 inference(trivial_inequality_removal,[status(thm)],[f790])).
% 1.62/1.09 thf(f790,plain,(
% 1.62/1.09 ($true = $false)),
% 1.62/1.09 inference(boolean_simplification,[status(thm)],[f789])).
% 1.62/1.09 thf(f789,plain,(
% 1.62/1.09 (((sK3 @ sK5 @ (sK2 @ sK4 @ sK6)) = (sK3 @ sK5 @ (sK2 @ sK4 @ sK6))) = $false)),
% 1.62/1.09 inference(backward_demodulation,[status(thm)],[f37,f786])).
% 1.62/1.09 thf(f786,plain,(
% 1.62/1.09 ( ! [X2 : a,X0 : a,X1 : a] : (((sK3 @ X0 @ (sK2 @ X2 @ (sK3 @ X0 @ X1))) = (sK3 @ X0 @ (sK2 @ X2 @ X1)))) )),
% 1.62/1.09 inference(forward_demodulation,[status(thm)],[f759,f35])).
% 1.62/1.09 thf(f35,plain,(
% 1.62/1.09 ( ! [X2 : a,X3 : a,X1 : a] : (((sK2 @ (sK3 @ X3 @ X2) @ (sK3 @ X3 @ X1)) = (sK3 @ X3 @ (sK2 @ X2 @ X1)))) )),
% 1.62/1.09 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.62/1.09 thf(f34,plain,(
% 1.62/1.09 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((sK3 @ X3 @ (sK2 @ X2 @ X1)) = (sK2 @ (sK3 @ X3 @ X2) @ (sK3 @ X3 @ X1))))) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.62/1.09 thf(f33,plain,(
% 1.62/1.09 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ Y0 @ (sK2 @ X2 @ X1)) = (sK2 @ (sK3 @ Y0 @ X2) @ (sK3 @ Y0 @ X1)))) @ X3))) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f32])).
% 1.62/1.09 thf(f32,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ (sK2 @ X2 @ X1)) = (sK2 @ (sK3 @ Y0 @ X2) @ (sK3 @ Y0 @ X1))))))) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.62/1.09 thf(f31,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ (sK2 @ Y0 @ X1)) = (sK2 @ (sK3 @ Y1 @ Y0) @ (sK3 @ Y1 @ X1)))))) @ X2))) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f30])).
% 1.62/1.09 thf(f30,plain,(
% 1.62/1.09 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ (sK2 @ Y0 @ X1)) = (sK2 @ (sK3 @ Y1 @ Y0) @ (sK3 @ Y1 @ X1))))))))) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.62/1.09 thf(f29,plain,(
% 1.62/1.09 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ (sK2 @ Y1 @ Y0)) = (sK2 @ (sK3 @ Y2 @ Y1) @ (sK3 @ Y2 @ Y0)))))))) @ X1))) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f28])).
% 1.62/1.09 thf(f28,plain,(
% 1.62/1.09 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ (sK2 @ Y1 @ Y0)) = (sK2 @ (sK3 @ Y2 @ Y1) @ (sK3 @ Y2 @ Y0))))))))))),
% 1.62/1.09 inference(boolean_simplification,[status(thm)],[f27])).
% 1.62/1.09 thf(f27,plain,(
% 1.62/1.09 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ (sK2 @ Y1 @ Y0)) = (sK2 @ (sK3 @ Y2 @ Y1) @ (sK3 @ Y2 @ Y0)))))))))))),
% 1.62/1.09 inference(backward_demodulation,[status(thm)],[f15,f26])).
% 1.62/1.09 thf(f26,plain,(
% 1.62/1.09 ((((((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y0) @ Y1) = (sK2 @ Y2 @ (sK2 @ Y0 @ Y1)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y1 @ Y2) @ Y0) = (sK3 @ Y1 @ (sK3 @ Y2 @ Y0)))))))))) = $true)),
% 1.62/1.09 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.62/1.09 thf(f15,plain,(
% 1.62/1.09 ($true = ((((((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y0) @ Y1) = (sK2 @ Y2 @ (sK2 @ Y0 @ Y1)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y1 @ Y2) @ Y0) = (sK3 @ Y1 @ (sK3 @ Y2 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ (sK2 @ Y1 @ Y0)) = (sK2 @ (sK3 @ Y2 @ Y1) @ (sK3 @ Y2 @ Y0)))))))))))),
% 1.62/1.09 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.62/1.09 thf(f13,plain,(
% 1.62/1.09 ((((((((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y0) @ Y1) = (sK2 @ Y2 @ (sK2 @ Y0 @ Y1)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y1 @ Y2) @ Y0) = (sK3 @ Y1 @ (sK3 @ Y2 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ (sK2 @ Y1 @ Y0)) = (sK2 @ (sK3 @ Y2 @ Y1) @ (sK3 @ Y2 @ Y0)))))))))) => (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ (sK3 @ Y1 @ Y2)) = (sK3 @ Y1 @ (sK2 @ Y0 @ (sK3 @ Y1 @ Y2))))))))))) = $false)),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.62/1.09 thf(f12,plain,(
% 1.62/1.09 (((^[Y0 : a > a > a]: (((((((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) = (sK2 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ (Y0 @ Y1 @ Y3)) = (Y0 @ (sK2 @ Y2 @ Y1) @ (sK2 @ Y2 @ Y3)))))))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y1) = Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (Y0 @ Y2 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1 @ Y1) = Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (sK2 @ Y1 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) = (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ (sK2 @ Y3 @ Y1) @ Y2) = (sK2 @ Y3 @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y0 @ Y2 @ Y3) @ Y1) = (Y0 @ Y2 @ (Y0 @ Y3 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ (sK2 @ Y2 @ Y1)) = (sK2 @ (Y0 @ Y3 @ Y2) @ (Y0 @ Y3 @ Y1)))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ (Y0 @ Y2 @ Y1) @ (Y0 @ Y2 @ Y3)) = (Y0 @ Y2 @ (sK2 @ Y1 @ (Y0 @ Y2 @ Y3)))))))))))) @ sK3) = $false)),
% 1.62/1.09 inference(sigma_clausification,[status(thm)],[f11])).
% 1.62/1.09 thf(f11,plain,(
% 1.62/1.09 ((!! @ (a > a > a) @ (^[Y0 : a > a > a]: (((((((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) = (sK2 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ (Y0 @ Y1 @ Y3)) = (Y0 @ (sK2 @ Y2 @ Y1) @ (sK2 @ Y2 @ Y3)))))))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y1) = Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (Y0 @ Y2 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1 @ Y1) = Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (sK2 @ Y1 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) = (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ (sK2 @ Y3 @ Y1) @ Y2) = (sK2 @ Y3 @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y0 @ Y2 @ Y3) @ Y1) = (Y0 @ Y2 @ (Y0 @ Y3 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ (sK2 @ Y2 @ Y1)) = (sK2 @ (Y0 @ Y3 @ Y2) @ (Y0 @ Y3 @ Y1)))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ (Y0 @ Y2 @ Y1) @ (Y0 @ Y2 @ Y3)) = (Y0 @ Y2 @ (sK2 @ Y1 @ (Y0 @ Y2 @ Y3))))))))))))) = $false)),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.62/1.09 thf(f10,plain,(
% 1.62/1.09 (((^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) = (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ (Y1 @ Y2 @ Y4)) = (Y1 @ (Y0 @ Y3 @ Y2) @ (Y0 @ Y3 @ Y4)))))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y2 @ Y3) @ Y3) = Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) = (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y0 @ Y4 @ Y2) @ Y3) = (Y0 @ Y4 @ (Y0 @ Y2 @ Y3)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ Y3 @ (Y1 @ Y4 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ (Y0 @ Y3 @ Y2)) = (Y0 @ (Y1 @ Y4 @ Y3) @ (Y1 @ Y4 @ Y2)))))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ (Y1 @ Y3 @ Y4)) = (Y1 @ Y3 @ (Y0 @ Y2 @ (Y1 @ Y3 @ Y4)))))))))))))) @ sK2) = $false)),
% 1.62/1.09 inference(sigma_clausification,[status(thm)],[f7])).
% 1.62/1.09 thf(f7,plain,(
% 1.62/1.09 ((!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) = (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ (Y1 @ Y2 @ Y4)) = (Y1 @ (Y0 @ Y3 @ Y2) @ (Y0 @ Y3 @ Y4)))))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y2 @ Y3) @ Y3) = Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) = (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y0 @ Y4 @ Y2) @ Y3) = (Y0 @ Y4 @ (Y0 @ Y2 @ Y3)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ Y3 @ (Y1 @ Y4 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ (Y0 @ Y3 @ Y2)) = (Y0 @ (Y1 @ Y4 @ Y3) @ (Y1 @ Y4 @ Y2)))))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ (Y1 @ Y3 @ Y4)) = (Y1 @ Y3 @ (Y0 @ Y2 @ (Y1 @ Y3 @ Y4))))))))))))))) = $false)),
% 1.62/1.09 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.62/1.09 thf(f6,plain,(
% 1.62/1.09 ((~ (!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) = (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ (Y1 @ Y2 @ Y4)) = (Y1 @ (Y0 @ Y3 @ Y2) @ (Y0 @ Y3 @ Y4)))))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y2 @ Y3) @ Y3) = Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) = (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y0 @ Y4 @ Y2) @ Y3) = (Y0 @ Y4 @ (Y0 @ Y2 @ Y3)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ Y3 @ (Y1 @ Y4 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ (Y0 @ Y3 @ Y2)) = (Y0 @ (Y1 @ Y4 @ Y3) @ (Y1 @ Y4 @ Y2)))))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ (Y1 @ Y3 @ Y4)) = (Y1 @ Y3 @ (Y0 @ Y2 @ (Y1 @ Y3 @ Y4)))))))))))))))) = $true)),
% 1.62/1.09 inference(cnf_transformation,[status(thm)],[f5])).
% 1.62/1.09 thf(f5,plain,(
% 1.62/1.09 ((~ (!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) = (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ (Y1 @ Y2 @ Y4)) = (Y1 @ (Y0 @ Y3 @ Y2) @ (Y0 @ Y3 @ Y4)))))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y2 @ Y3) @ Y3) = Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) = (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y0 @ Y4 @ Y2) @ Y3) = (Y0 @ Y4 @ (Y0 @ Y2 @ Y3)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ Y3 @ (Y1 @ Y4 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ (Y0 @ Y3 @ Y2)) = (Y0 @ (Y1 @ Y4 @ Y3) @ (Y1 @ Y4 @ Y2)))))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ (Y1 @ Y3 @ Y4)) = (Y1 @ Y3 @ (Y0 @ Y2 @ (Y1 @ Y3 @ Y4)))))))))))))))) = $true)),
% 1.62/1.09 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.09 thf(f4,plain,(
% 1.62/1.09 ~! [X0 : a > a > a,X1 : a > a > a] : ((! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4))) & ! [X5 : a,X6 : a,X7 : a] : ((X0 @ (X0 @ X6 @ X5) @ X7) = (X0 @ X6 @ (X0 @ X5 @ X7))) & ! [X8 : a,X9 : a,X10 : a] : ((X1 @ (X1 @ X8 @ X10) @ X9) = (X1 @ X8 @ (X1 @ X10 @ X9))) & ! [X11 : a,X12 : a] : ((X0 @ X12 @ X11) = (X0 @ X11 @ X12)) & ! [X13 : a,X14 : a] : ((X0 @ (X1 @ X14 @ X13) @ X13) = X13) & ! [X15 : a] : ((X0 @ X15 @ X15) = X15) & ! [X16 : a,X17 : a] : ((X1 @ (X0 @ X16 @ X17) @ X17) = X17) & ! [X18 : a] : ((X1 @ X18 @ X18) = X18) & ! [X19 : a,X20 : a,X21 : a] : ((X1 @ X20 @ (X0 @ X21 @ X19)) = (X0 @ (X1 @ X20 @ X21) @ (X1 @ X20 @ X19))) & ! [X22 : a,X23 : a] : ((X1 @ X22 @ X23) = (X1 @ X23 @ X22))) => ! [X24 : a,X25 : a,X26 : a] : ((X1 @ (X0 @ X25 @ X26) @ (X0 @ X25 @ X24)) = (X0 @ X25 @ (X1 @ X26 @ (X0 @ X25 @ X24)))))),
% 1.62/1.09 inference(rectify,[status(thm)],[f2])).
% 1.62/1.09 thf(f2,negated_conjecture,(
% 1.62/1.09 ~! [X0 : a > a > a,X1 : a > a > a] : ((! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4))) & ! [X3 : a,X2 : a,X4 : a] : ((X0 @ (X0 @ X2 @ X3) @ X4) = (X0 @ X2 @ (X0 @ X3 @ X4))) & ! [X2 : a,X4 : a,X3 : a] : ((X1 @ (X1 @ X2 @ X3) @ X4) = (X1 @ X2 @ (X1 @ X3 @ X4))) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) = (X0 @ X3 @ X2)) & ! [X3 : a,X2 : a] : ((X0 @ (X1 @ X2 @ X3) @ X3) = X3) & ! [X2 : a] : ((X0 @ X2 @ X2) = X2) & ! [X2 : a,X3 : a] : ((X1 @ (X0 @ X2 @ X3) @ X3) = X3) & ! [X2 : a] : ((X1 @ X2 @ X2) = X2) & ! [X4 : a,X2 : a,X3 : a] : ((X1 @ X2 @ (X0 @ X3 @ X4)) = (X0 @ (X1 @ X2 @ X3) @ (X1 @ X2 @ X4))) & ! [X3 : a,X2 : a] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2))) => ! [X4 : a,X2 : a,X3 : a] : ((X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4)) = (X0 @ X2 @ (X1 @ X3 @ (X0 @ X2 @ X4)))))),
% 1.62/1.09 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.09 thf(f1,conjecture,(
% 1.62/1.09 ! [X0 : a > a > a,X1 : a > a > a] : ((! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4))) & ! [X3 : a,X2 : a,X4 : a] : ((X0 @ (X0 @ X2 @ X3) @ X4) = (X0 @ X2 @ (X0 @ X3 @ X4))) & ! [X2 : a,X4 : a,X3 : a] : ((X1 @ (X1 @ X2 @ X3) @ X4) = (X1 @ X2 @ (X1 @ X3 @ X4))) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) = (X0 @ X3 @ X2)) & ! [X3 : a,X2 : a] : ((X0 @ (X1 @ X2 @ X3) @ X3) = X3) & ! [X2 : a] : ((X0 @ X2 @ X2) = X2) & ! [X2 : a,X3 : a] : ((X1 @ (X0 @ X2 @ X3) @ X3) = X3) & ! [X2 : a] : ((X1 @ X2 @ X2) = X2) & ! [X4 : a,X2 : a,X3 : a] : ((X1 @ X2 @ (X0 @ X3 @ X4)) = (X0 @ (X1 @ X2 @ X3) @ (X1 @ X2 @ X4))) & ! [X3 : a,X2 : a] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2))) => ! [X4 : a,X2 : a,X3 : a] : ((X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4)) = (X0 @ X2 @ (X1 @ X3 @ (X0 @ X2 @ X4)))))),
% 1.62/1.09 file('/export/starexec/sandbox/tmp/tmp.Q33ztibo3p/DTF2THF_25816.p',cMODULAR_THM_DEF2_pme)).
% 1.62/1.09 thf(f759,plain,(
% 1.62/1.09 ( ! [X2 : a,X0 : a,X1 : a] : (((sK3 @ X0 @ (sK2 @ X2 @ (sK3 @ X0 @ X1))) = (sK2 @ (sK3 @ X0 @ X2) @ (sK3 @ X0 @ X1)))) )),
% 1.62/1.09 inference(superposition,[status(thm)],[f35,f345])).
% 1.62/1.09 thf(f345,plain,(
% 1.62/1.09 ( ! [X0 : a,X1 : a] : (((sK3 @ X0 @ (sK3 @ X0 @ X1)) = (sK3 @ X0 @ X1))) )),
% 1.62/1.09 inference(superposition,[status(thm)],[f276,f204])).
% 1.62/1.09 thf(f204,plain,(
% 1.62/1.09 ( ! [X0 : a] : (((sK3 @ X0 @ X0) = X0)) )),
% 1.62/1.09 inference(forward_demodulation,[status(thm)],[f189,f81])).
% 1.62/1.09 thf(f81,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : (((sK3 @ X2 @ (sK2 @ X1 @ X2)) = X2)) )),
% 1.62/1.09 inference(equality_proxy_clausification,[status(thm)],[f68])).
% 1.62/1.09 thf(f68,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : ((((sK3 @ X2 @ (sK2 @ X1 @ X2)) = X2) = $true)) )),
% 1.62/1.09 inference(forward_demodulation,[status(thm)],[f67,f65])).
% 1.62/1.09 thf(f65,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : (((sK3 @ X1 @ X2) = (sK3 @ X2 @ X1))) )),
% 1.62/1.09 inference(equality_proxy_clausification,[status(thm)],[f62])).
% 1.62/1.09 thf(f62,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X1 @ X2) = (sK3 @ X2 @ X1)))) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.62/1.09 thf(f61,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK3 @ X1 @ Y0) = (sK3 @ Y0 @ X1))) @ X2) = $true)) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f56])).
% 1.62/1.09 thf(f56,plain,(
% 1.62/1.09 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) = (sK3 @ Y0 @ X1)))))) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.62/1.09 thf(f55,plain,(
% 1.62/1.09 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))) @ X1))) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f51])).
% 1.62/1.09 thf(f51,plain,(
% 1.62/1.09 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0)))))) = $true)),
% 1.62/1.09 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.62/1.09 thf(f48,plain,(
% 1.62/1.09 ($true = (((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))))),
% 1.62/1.09 inference(boolean_simplification,[status(thm)],[f47])).
% 1.62/1.09 thf(f47,plain,(
% 1.62/1.09 ($true = ((((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & $true))),
% 1.62/1.09 inference(backward_demodulation,[status(thm)],[f44,f45])).
% 1.62/1.09 thf(f45,plain,(
% 1.62/1.09 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y0) @ Y1) = (sK2 @ Y2 @ (sK2 @ Y0 @ Y1))))))))))),
% 1.62/1.09 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.62/1.09 thf(f44,plain,(
% 1.62/1.09 ($true = ((((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y0) @ Y1) = (sK2 @ Y2 @ (sK2 @ Y0 @ Y1)))))))))))),
% 1.62/1.09 inference(boolean_simplification,[status(thm)],[f43])).
% 1.62/1.09 thf(f43,plain,(
% 1.62/1.09 ($true = (((((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK2 @ Y2 @ Y0) @ Y1) = (sK2 @ Y2 @ (sK2 @ Y0 @ Y1)))))))))) & $true))),
% 1.62/1.09 inference(backward_demodulation,[status(thm)],[f26,f41])).
% 1.62/1.09 thf(f41,plain,(
% 1.62/1.09 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y1 @ Y2) @ Y0) = (sK3 @ Y1 @ (sK3 @ Y2 @ Y0))))))))))),
% 1.62/1.09 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.62/1.09 thf(f67,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ (sK2 @ X1 @ X2) @ X2) = X2))) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.62/1.09 thf(f66,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK3 @ (sK2 @ X1 @ Y0) @ Y0) = Y0)) @ X2) = $true)) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f64])).
% 1.62/1.09 thf(f64,plain,(
% 1.62/1.09 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ (sK2 @ X1 @ Y0) @ Y0) = Y0))))) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.62/1.09 thf(f63,plain,(
% 1.62/1.09 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))) @ X1))) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f60])).
% 1.62/1.09 thf(f60,plain,(
% 1.62/1.09 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1))))))),
% 1.62/1.09 inference(boolean_simplification,[status(thm)],[f59])).
% 1.62/1.09 thf(f59,plain,(
% 1.62/1.09 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))))),
% 1.62/1.09 inference(backward_demodulation,[status(thm)],[f54,f58])).
% 1.62/1.09 thf(f58,plain,(
% 1.62/1.09 ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) = $true)),
% 1.62/1.09 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.62/1.09 thf(f54,plain,(
% 1.62/1.09 ($true = ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))))),
% 1.62/1.09 inference(boolean_simplification,[status(thm)],[f53])).
% 1.62/1.09 thf(f53,plain,(
% 1.62/1.09 ($true = (((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) = (sK2 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK3 @ Y0 @ Y2)) = (sK3 @ (sK2 @ Y1 @ Y0) @ (sK2 @ Y1 @ Y2)))))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y0 @ Y1) @ Y1) = Y1)))))) & $true))),
% 1.62/1.09 inference(backward_demodulation,[status(thm)],[f48,f51])).
% 1.62/1.09 thf(f189,plain,(
% 1.62/1.09 ( ! [X0 : a,X1 : a] : (((sK3 @ X0 @ (sK3 @ X0 @ (sK2 @ X1 @ X0))) = X0)) )),
% 1.62/1.09 inference(superposition,[status(thm)],[f181,f35])).
% 1.62/1.09 thf(f181,plain,(
% 1.62/1.09 ( ! [X0 : a,X1 : a] : (((sK3 @ X0 @ (sK2 @ X1 @ (sK3 @ X0 @ X0))) = X0)) )),
% 1.62/1.09 inference(forward_demodulation,[status(thm)],[f180,f81])).
% 1.62/1.09 thf(f180,plain,(
% 1.62/1.09 ( ! [X0 : a,X1 : a] : (((sK3 @ X0 @ (sK2 @ X1 @ (sK3 @ X0 @ X0))) = (sK3 @ X0 @ (sK2 @ X1 @ X0)))) )),
% 1.62/1.09 inference(forward_demodulation,[status(thm)],[f172,f35])).
% 1.62/1.09 thf(f172,plain,(
% 1.62/1.09 ( ! [X0 : a,X1 : a] : (((sK3 @ X0 @ (sK2 @ X1 @ (sK3 @ X0 @ X0))) = (sK2 @ (sK3 @ X0 @ X1) @ (sK3 @ X0 @ X0)))) )),
% 1.62/1.09 inference(superposition,[status(thm)],[f35,f125])).
% 1.62/1.09 thf(f125,plain,(
% 1.62/1.09 ( ! [X0 : a] : (((sK3 @ X0 @ X0) = (sK3 @ X0 @ (sK3 @ X0 @ X0)))) )),
% 1.62/1.09 inference(superposition,[status(thm)],[f65,f99])).
% 1.62/1.09 thf(f99,plain,(
% 1.62/1.09 ( ! [X0 : a] : (((sK3 @ X0 @ X0) = (sK3 @ (sK3 @ X0 @ X0) @ X0))) )),
% 1.62/1.09 inference(superposition,[status(thm)],[f85,f81])).
% 1.62/1.09 thf(f85,plain,(
% 1.62/1.09 ( ! [X2 : a,X0 : a,X1 : a] : (((sK3 @ X0 @ X2) = (sK3 @ (sK3 @ X0 @ X2) @ (sK3 @ X0 @ (sK2 @ X1 @ X2))))) )),
% 1.62/1.09 inference(superposition,[status(thm)],[f81,f35])).
% 1.62/1.09 thf(f276,plain,(
% 1.62/1.09 ( ! [X2 : a,X3 : a,X1 : a] : (((sK3 @ X2 @ (sK3 @ X3 @ X1)) = (sK3 @ (sK3 @ X2 @ X3) @ X1))) )),
% 1.62/1.09 inference(equality_proxy_clausification,[status(thm)],[f263])).
% 1.62/1.09 thf(f263,plain,(
% 1.62/1.09 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((sK3 @ (sK3 @ X2 @ X3) @ X1) = (sK3 @ X2 @ (sK3 @ X3 @ X1))))) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f262])).
% 1.62/1.09 thf(f262,plain,(
% 1.62/1.09 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ (sK3 @ X2 @ Y0) @ X1) = (sK3 @ X2 @ (sK3 @ Y0 @ X1)))) @ X3))) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f188])).
% 1.62/1.09 thf(f188,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK3 @ (sK3 @ X2 @ Y0) @ X1) = (sK3 @ X2 @ (sK3 @ Y0 @ X1))))) = $true)) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f187])).
% 1.62/1.09 thf(f187,plain,(
% 1.62/1.09 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK3 @ Y0 @ Y1) @ X1) = (sK3 @ Y0 @ (sK3 @ Y1 @ X1)))))) @ X2))) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f50])).
% 1.62/1.09 thf(f50,plain,(
% 1.62/1.09 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK3 @ Y0 @ Y1) @ X1) = (sK3 @ Y0 @ (sK3 @ Y1 @ X1))))))) = $true)) )),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.62/1.09 thf(f49,plain,(
% 1.62/1.09 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK3 @ Y1 @ Y2) @ Y0) = (sK3 @ Y1 @ (sK3 @ Y2 @ Y0)))))))) @ X1))) )),
% 1.62/1.09 inference(pi_clausification,[status(thm)],[f41])).
% 1.62/1.09 thf(f37,plain,(
% 1.62/1.09 (((sK3 @ sK5 @ (sK2 @ sK4 @ sK6)) = (sK3 @ sK5 @ (sK2 @ sK4 @ (sK3 @ sK5 @ sK6)))) = $false)),
% 1.62/1.09 inference(backward_demodulation,[status(thm)],[f23,f35])).
% 1.62/1.09 thf(f23,plain,(
% 1.62/1.09 (((sK2 @ (sK3 @ sK5 @ sK4) @ (sK3 @ sK5 @ sK6)) = (sK3 @ sK5 @ (sK2 @ sK4 @ (sK3 @ sK5 @ sK6)))) = $false)),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.62/1.09 thf(f22,plain,(
% 1.62/1.09 (((^[Y0 : a]: ((sK2 @ (sK3 @ sK5 @ sK4) @ (sK3 @ sK5 @ Y0)) = (sK3 @ sK5 @ (sK2 @ sK4 @ (sK3 @ sK5 @ Y0))))) @ sK6) = $false)),
% 1.62/1.09 inference(sigma_clausification,[status(thm)],[f21])).
% 1.62/1.09 thf(f21,plain,(
% 1.62/1.09 ((!! @ a @ (^[Y0 : a]: ((sK2 @ (sK3 @ sK5 @ sK4) @ (sK3 @ sK5 @ Y0)) = (sK3 @ sK5 @ (sK2 @ sK4 @ (sK3 @ sK5 @ Y0)))))) = $false)),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.62/1.09 thf(f20,plain,(
% 1.62/1.09 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y0 @ sK4) @ (sK3 @ Y0 @ Y1)) = (sK3 @ Y0 @ (sK2 @ sK4 @ (sK3 @ Y0 @ Y1))))))) @ sK5) = $false)),
% 1.62/1.09 inference(sigma_clausification,[status(thm)],[f19])).
% 1.62/1.09 thf(f19,plain,(
% 1.62/1.09 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y0 @ sK4) @ (sK3 @ Y0 @ Y1)) = (sK3 @ Y0 @ (sK2 @ sK4 @ (sK3 @ Y0 @ Y1)))))))) = $false)),
% 1.62/1.09 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.62/1.09 thf(f18,plain,(
% 1.62/1.09 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ (sK3 @ Y1 @ Y2)) = (sK3 @ Y1 @ (sK2 @ Y0 @ (sK3 @ Y1 @ Y2))))))))) @ sK4) = $false)),
% 1.62/1.09 inference(sigma_clausification,[status(thm)],[f17])).
% 1.62/1.09 thf(f17,plain,(
% 1.62/1.09 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ (sK3 @ Y1 @ Y2)) = (sK3 @ Y1 @ (sK2 @ Y0 @ (sK3 @ Y1 @ Y2)))))))))) = $false)),
% 1.62/1.09 inference(boolean_simplification,[status(thm)],[f16])).
% 1.62/1.09 thf(f16,plain,(
% 1.62/1.09 (($true => (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ (sK3 @ Y1 @ Y2)) = (sK3 @ Y1 @ (sK2 @ Y0 @ (sK3 @ Y1 @ Y2))))))))))) = $false)),
% 1.62/1.09 inference(backward_demodulation,[status(thm)],[f13,f15])).
% 1.62/1.09 % SZS output end Proof for DTF2THF_25816
% 1.62/1.09 % (26019)------------------------------
% 1.62/1.09 % (26019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.09 % (26019)Termination reason: Refutation
% 1.62/1.09
% 1.62/1.09 % (26019)Memory used [KB]: 6524
% 1.62/1.09 % (26019)Time elapsed: 0.141 s
% 1.62/1.09 % (26019)Instructions burned: 293 (million)
% 1.62/1.09 % (26019)------------------------------
% 1.62/1.09 % (26019)------------------------------
% 1.62/1.09 % (26004)Success in time 0.157 s
%------------------------------------------------------------------------------