TSTP Solution File: SEV122^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV122^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n018.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 : Mon Jun 24 16:01:54 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 8
% Syntax : Number of formulae : 92 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 704 ( 159 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1572 ( 63 ~; 118 |; 51 &;1017 @)
% ( 6 <=>; 117 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 509 ( 509 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 22 usr; 12 con; 0-3 aty)
% ( 135 !!; 65 ??; 0 @@+; 0 @@-)
% Number of variables : 422 ( 268 ^ 146 !; 8 ?; 422 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_12,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_14,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK3: a ).
thf(func_def_17,type,
sK4: a ).
thf(func_def_18,type,
sK5: a > a > $o ).
thf(func_def_19,type,
sK6: a > a > $o ).
thf(func_def_20,type,
sK7: a > a > $o ).
thf(func_def_21,type,
sK8: a > a > $o ).
thf(func_def_22,type,
sK9: ( a > a > $o ) > a ).
thf(func_def_23,type,
sK10: ( a > a > $o ) > a ).
thf(func_def_24,type,
sK11: ( a > a > $o ) > a ).
thf(func_def_25,type,
sK12: ( a > a > $o ) > a ).
thf(func_def_26,type,
sK13: ( a > a > $o ) > a > a > $o ).
thf(func_def_27,type,
sK14: ( a > a > $o ) > a > a > $o ).
thf(func_def_28,type,
sK15: ( a > a > $o ) > a ).
thf(func_def_29,type,
sK16: ( a > a > $o ) > a > a > $o ).
thf(f388,plain,
$false,
inference(avatar_sat_refutation,[],[f129,f133,f164,f168,f247,f293,f387]) ).
thf(f387,plain,
( ~ spl1_15
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f386]) ).
thf(f386,plain,
( $false
| ~ spl1_15
| ~ spl1_17 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f385,plain,
( ( $false = $true )
| ~ spl1_15
| ~ spl1_17 ),
inference(forward_demodulation,[],[f378,f317]) ).
thf(f317,plain,
( ! [X0: a > a > $o] :
( ( X0 @ sK3 @ sK4 )
= $false )
| ~ spl1_15
| ~ spl1_17 ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f308,plain,
( ! [X0: a > a > $o] :
( ( $false = $true )
| ( ( X0 @ sK3 @ sK4 )
= $false ) )
| ~ spl1_15
| ~ spl1_17 ),
inference(superposition,[],[f160,f167]) ).
thf(f167,plain,
( ! [X6: a > a > $o,X4: a,X5: a] :
( ( ( sK6 @ X4 @ X5 )
= $true )
| ( ( X6 @ X4 @ X5 )
= $false ) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f166]) ).
thf(f166,plain,
( spl1_17
<=> ! [X6: a > a > $o,X4: a,X5: a] :
( ( ( X6 @ X4 @ X5 )
= $false )
| ( ( sK6 @ X4 @ X5 )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
thf(f160,plain,
( ( ( sK6 @ sK3 @ sK4 )
= $false )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f158,plain,
( spl1_15
<=> ( ( sK6 @ sK3 @ sK4 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
thf(f378,plain,
( ! [X3: a > a > $o] :
( $true
= ( X3 @ sK3 @ sK4 ) )
| ~ spl1_15
| ~ spl1_17 ),
inference(not_proxy_clausification,[],[f377]) ).
thf(f377,plain,
( ! [X3: a > a > $o] :
( ( ~ ( X3 @ sK3 @ sK4 ) )
= $false )
| ~ spl1_15
| ~ spl1_17 ),
inference(beta_eta_normalization,[],[f354]) ).
thf(f354,plain,
( ! [X3: a > a > $o] :
( ( ^ [Y0: a,Y1: a] :
~ ( X3 @ Y0 @ Y1 )
@ sK3
@ sK4 )
= $false )
| ~ spl1_15
| ~ spl1_17 ),
inference(primitive_instantiation,[],[f317]) ).
thf(f293,plain,
( ~ spl1_7
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[],[f292]) ).
thf(f292,plain,
( $false
| ~ spl1_7
| ~ spl1_9 ),
inference(trivial_inequality_removal,[],[f277]) ).
thf(f277,plain,
( ( $false = $true )
| ~ spl1_7
| ~ spl1_9 ),
inference(superposition,[],[f274,f124]) ).
thf(f124,plain,
( ( ( sK8 @ sK3 @ sK4 )
= $false )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f122,plain,
( spl1_7
<=> ( ( sK8 @ sK3 @ sK4 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
thf(f274,plain,
( ! [X2: a,X1: a] :
( ( sK8 @ X1 @ X2 )
= $true )
| ~ spl1_9 ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f273,plain,
( ! [X2: a,X1: a] :
( ( ( sK8 @ X1 @ X2 )
= $true )
| ( $false = $true ) )
| ~ spl1_9 ),
inference(beta_eta_normalization,[],[f253]) ).
thf(f253,plain,
( ! [X2: a,X1: a] :
( ( ( sK8 @ X1 @ X2 )
= $true )
| ( ( ^ [Y0: a,Y1: a] : $true
@ X1
@ X2 )
= $false ) )
| ~ spl1_9 ),
inference(primitive_instantiation,[],[f132]) ).
thf(f132,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK8 @ X1 @ X2 )
= $true ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f131]) ).
thf(f131,plain,
( spl1_9
<=> ! [X2: a,X1: a,X3: a > a > $o] :
( ( ( sK8 @ X1 @ X2 )
= $true )
| ( $false
= ( X3 @ X1 @ X2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
thf(f247,plain,
( ~ spl1_8
| ~ spl1_16 ),
inference(avatar_contradiction_clause,[],[f246]) ).
thf(f246,plain,
( $false
| ~ spl1_8
| ~ spl1_16 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f238,plain,
( ( $false = $true )
| ~ spl1_8
| ~ spl1_16 ),
inference(superposition,[],[f128,f190]) ).
thf(f190,plain,
( ! [X2: a,X1: a] :
( ( sK5 @ X2 @ X1 )
= $true )
| ~ spl1_16 ),
inference(subsumption_resolution,[],[f186,f189]) ).
thf(f189,plain,
( ! [X2: a,X1: a] :
( ( X1 != X2 )
| ( ( sK5 @ X2 @ X1 )
= $true ) )
| ~ spl1_16 ),
inference(equality_proxy_clausification,[],[f188]) ).
thf(f188,plain,
( ! [X2: a,X1: a] :
( ( $false
= ( X1 = X2 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) )
| ~ spl1_16 ),
inference(beta_eta_normalization,[],[f174]) ).
thf(f174,plain,
( ! [X2: a,X1: a] :
( ( ( sK5 @ X2 @ X1 )
= $true )
| ( ( ^ [Y0: a,Y1: a] : ( Y1 = Y0 )
@ X2
@ X1 )
= $false ) )
| ~ spl1_16 ),
inference(primitive_instantiation,[],[f163]) ).
thf(f163,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) )
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f162]) ).
thf(f162,plain,
( spl1_16
<=> ! [X2: a,X1: a,X3: a > a > $o] :
( ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
thf(f186,plain,
( ! [X2: a,X1: a] :
( ( X1 = X2 )
| ( ( sK5 @ X2 @ X1 )
= $true ) )
| ~ spl1_16 ),
inference(equality_proxy_clausification,[],[f185]) ).
thf(f185,plain,
( ! [X2: a,X1: a] :
( ( ( sK5 @ X2 @ X1 )
= $true )
| ( $true
= ( X1 = X2 ) ) )
| ~ spl1_16 ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f184,plain,
( ! [X2: a,X1: a] :
( ( ( sK5 @ X2 @ X1 )
= $true )
| ( ( X1 != X2 )
= $false ) )
| ~ spl1_16 ),
inference(beta_eta_normalization,[],[f175]) ).
thf(f175,plain,
( ! [X2: a,X1: a] :
( ( $false
= ( ^ [Y0: a,Y1: a] : ( Y1 != Y0 )
@ X2
@ X1 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) )
| ~ spl1_16 ),
inference(primitive_instantiation,[],[f163]) ).
thf(f128,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f126,plain,
( spl1_8
<=> ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
thf(f168,plain,
( spl1_16
| spl1_17 ),
inference(avatar_split_clause,[],[f42,f166,f162]) ).
thf(f42,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X4: a,X5: a] :
( ( ( X6 @ X4 @ X5 )
= $false )
| ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK6 @ X4 @ X5 )
= $true )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[],[f41]) ).
thf(f41,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X4: a,X5: a] :
( ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK6 @ X4 @ X5 )
= $true )
| ( ( ^ [Y0: a > a > $o] : ( Y0 @ X4 @ X5 )
@ X6 )
= $false )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(pi_clausification,[],[f40]) ).
thf(f40,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a,X5: a] :
( ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK6 @ X4 @ X5 )
= $true )
| ( $false
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X4 @ X5 ) ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[],[f39]) ).
thf(f39,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a,X5: a] :
( ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X4 @ X5 ) )
=> ( sK6 @ X4 @ X5 ) )
= $true )
| ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[],[f38]) ).
thf(f38,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a,X5: a] :
( ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X4 @ Y0 ) )
=> ( sK6 @ X4 @ Y0 ) )
@ X5 )
= $true )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(pi_clausification,[],[f37]) ).
thf(f37,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X4 @ Y0 ) )
=> ( sK6 @ X4 @ Y0 ) ) ) )
| ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a] :
( ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X4 )
= $true )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(pi_clausification,[],[f34]) ).
thf(f34,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK5 @ X2 @ X1 )
= $true )
| ( $false
= ( X3 @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( ( sK0 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f31,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( ( ( sK0 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK3 @ sK4 ) )
= $false )
| ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[],[f30]) ).
thf(f30,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( ( ( sK0 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK3 @ sK4 ) )
= $false )
| ( ( sK5 @ X2 @ X1 )
= $true )
| ( ( ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X1 )
@ X3 )
= $false ) ),
inference(pi_clausification,[],[f29]) ).
thf(f29,plain,
! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X1 ) )
= $false )
| ( ( ( ( sK0 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK3 @ sK4 ) )
= $false )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[],[f28]) ).
thf(f28,plain,
! [X2: a,X1: a] :
( ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X1 ) )
=> ( sK5 @ X2 @ X1 ) )
= $true )
| ( ( ( ( sK0 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK3 @ sK4 ) )
= $false ) ),
inference(beta_eta_normalization,[],[f27]) ).
thf(f27,plain,
! [X2: a,X1: a] :
( ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X1 ) )
=> ( sK5 @ X2 @ X1 ) )
= $true )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) )
@ sK6 ) ) ),
inference(sigma_clausification,[],[f26]) ).
thf(f26,plain,
! [X2: a,X1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X1 ) )
=> ( sK5 @ X2 @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f25]) ).
thf(f25,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ Y0 @ X1 ) )
=> ( sK5 @ Y0 @ X1 ) )
@ X2 ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false ) ),
inference(pi_clausification,[],[f24]) ).
thf(f24,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ Y0 @ X1 ) )
=> ( sK5 @ Y0 @ X1 ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f23]) ).
thf(f23,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false ) ),
inference(pi_clausification,[],[f22]) ).
thf(f22,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f20,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( sK0 @ sK5 ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f18]) ).
thf(f18,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( sK0 @ sK5 ) )
=> ( sK5 @ sK3 @ sK4 ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f17]) ).
thf(f17,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false )
| ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ sK3 @ sK4 ) )
@ sK5 )
= $false ) ),
inference(sigma_clausification,[],[f16]) ).
thf(f16,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ sK3 @ sK4 ) ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f14]) ).
thf(f14,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ sK3 @ sK4 ) ) ) ),
inference(beta_eta_normalization,[],[f13]) ).
thf(f13,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK0 @ Y1 ) )
=> ( Y1 @ sK3 @ Y0 ) ) )
@ sK4 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK0 @ Y1 ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK3 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
=> ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f7,plain,
? [X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,plain,
~ ! [X1: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( X1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X1: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] : ( X7 @ X6 @ X5 )
=> ( X4 @ X6 @ X5 ) )
& ( X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ( ( X1 @ X10 )
& ! [X11: a,X12: a] :
( ? [X13: a > a > $o] : ( X13 @ X11 @ X12 )
=> ( X10 @ X11 @ X12 ) ) )
=> ( X10 @ X8 @ X9 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM530_pme) ).
thf(f164,plain,
( spl1_15
| spl1_16 ),
inference(avatar_split_clause,[],[f32,f162,f158]) ).
thf(f32,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK6 @ sK3 @ sK4 )
= $false )
| ( $false
= ( X3 @ X2 @ X1 ) )
| ( ( sK5 @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f133,plain,
( spl1_8
| spl1_9 ),
inference(avatar_split_clause,[],[f68,f131,f126]) ).
thf(f68,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK8 @ X1 @ X2 )
= $true )
| ( $false
= ( X3 @ X1 @ X2 ) )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(beta_eta_normalization,[],[f67]) ).
thf(f67,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( ( ^ [Y0: a > a > $o] : ( Y0 @ X1 @ X2 )
@ X3 )
= $false )
| ( ( sK8 @ X1 @ X2 )
= $true ) ),
inference(pi_clausification,[],[f66]) ).
thf(f66,plain,
! [X2: a,X1: a] :
( ( ( sK8 @ X1 @ X2 )
= $true )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X1 @ X2 ) )
= $false )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(binary_proxy_clausification,[],[f65]) ).
thf(f65,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X1 @ X2 ) )
=> ( sK8 @ X1 @ X2 ) ) )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(beta_eta_normalization,[],[f64]) ).
thf(f64,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X1 @ Y0 ) )
=> ( sK8 @ X1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f63]) ).
thf(f63,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X1 @ Y0 ) )
=> ( sK8 @ X1 @ Y0 ) ) )
= $true )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(beta_eta_normalization,[],[f62]) ).
thf(f62,plain,
! [X1: a] :
( ( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(pi_clausification,[],[f60]) ).
thf(f60,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f59]) ).
thf(f59,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( ( ( sK0 @ sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f57]) ).
thf(f57,plain,
( ( ( ( ( sK0 @ sK8 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
=> ( sK8 @ sK3 @ sK4 ) )
= $false )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(beta_eta_normalization,[],[f56]) ).
thf(f56,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) )
@ sK8 )
= $false )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(sigma_clausification,[],[f19]) ).
thf(f19,plain,
( ( $false
= ( sK5 @ sK3 @ sK4 ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f18]) ).
thf(f129,plain,
( spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f58,f126,f122]) ).
thf(f58,plain,
( ( ( sK8 @ sK3 @ sK4 )
= $false )
| ( $false
= ( sK5 @ sK3 @ sK4 ) ) ),
inference(binary_proxy_clausification,[],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV122^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:22:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 This is a TH0_THM_EQU_NAR problem
% 0.12/0.36 Running higher-order theorem proving
% 0.12/0.36 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.22/0.38 % (827)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 theBenchmark for (2999ds/27Mi)
% 0.22/0.38 % (826)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 theBenchmark for (2999ds/4Mi)
% 0.22/0.38 % (829)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (830)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.22/0.38 % (825)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.38 % (831)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38 % (829)Instruction limit reached!
% 0.22/0.38 % (829)------------------------------
% 0.22/0.38 % (829)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (829)Termination reason: Unknown
% 0.22/0.38 % (829)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (829)Memory used [KB]: 895
% 0.22/0.38 % (829)Time elapsed: 0.004 s
% 0.22/0.38 % (829)Instructions burned: 2 (million)
% 0.22/0.38 % (829)------------------------------
% 0.22/0.38 % (829)------------------------------
% 0.22/0.38 % (828)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (826)Instruction limit reached!
% 0.22/0.38 % (826)------------------------------
% 0.22/0.38 % (826)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (826)Termination reason: Unknown
% 0.22/0.38 % (826)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (826)Memory used [KB]: 5500
% 0.22/0.38 % (826)Time elapsed: 0.005 s
% 0.22/0.38 % (826)Instructions burned: 4 (million)
% 0.22/0.38 % (826)------------------------------
% 0.22/0.38 % (826)------------------------------
% 0.22/0.38 % (828)Instruction limit reached!
% 0.22/0.38 % (828)------------------------------
% 0.22/0.38 % (828)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (828)Termination reason: Unknown
% 0.22/0.38 % (828)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (828)Memory used [KB]: 5500
% 0.22/0.38 % (828)Time elapsed: 0.004 s
% 0.22/0.38 % (828)Instructions burned: 2 (million)
% 0.22/0.38 % (828)------------------------------
% 0.22/0.38 % (828)------------------------------
% 0.22/0.39 % (831)Instruction limit reached!
% 0.22/0.39 % (831)------------------------------
% 0.22/0.39 % (831)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (831)Termination reason: Unknown
% 0.22/0.39 % (831)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (831)Memory used [KB]: 5628
% 0.22/0.39 % (831)Time elapsed: 0.014 s
% 0.22/0.39 % (831)Instructions burned: 18 (million)
% 0.22/0.39 % (831)------------------------------
% 0.22/0.39 % (831)------------------------------
% 0.22/0.40 % (830)First to succeed.
% 0.22/0.40 % (839)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40 % (827)Instruction limit reached!
% 0.22/0.40 % (827)------------------------------
% 0.22/0.40 % (827)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (827)Termination reason: Unknown
% 0.22/0.40 % (827)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (827)Memory used [KB]: 5628
% 0.22/0.40 % (827)Time elapsed: 0.021 s
% 0.22/0.40 % (827)Instructions burned: 27 (million)
% 0.22/0.40 % (827)------------------------------
% 0.22/0.40 % (827)------------------------------
% 0.22/0.40 % (841)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 theBenchmark for (2999ds/37Mi)
% 0.22/0.40 % (844)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 theBenchmark for (2999ds/15Mi)
% 0.22/0.40 % (839)Also succeeded, but the first one will report.
% 0.22/0.40 % (830)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (830)------------------------------
% 0.22/0.40 % (830)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (830)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (830)Memory used [KB]: 5756
% 0.22/0.40 % (830)Time elapsed: 0.024 s
% 0.22/0.40 % (830)Instructions burned: 24 (million)
% 0.22/0.40 % (830)------------------------------
% 0.22/0.40 % (830)------------------------------
% 0.22/0.40 % (821)Success in time 0.038 s
%------------------------------------------------------------------------------