TSTP Solution File: ALG290^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG290^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n026.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 May 20 18:20:51 EDT 2024
% Result : Theorem 2.14s 0.66s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 41
% Syntax : Number of formulae : 207 ( 8 unt; 34 typ; 0 def)
% Number of atoms : 1604 ( 338 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 4286 ( 301 ~; 304 |; 383 &;2396 @)
% ( 9 <=>; 397 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 248 ( 248 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 38 usr; 28 con; 0-2 aty)
% ( 329 !!; 167 ??; 0 @@+; 0 @@-)
% Number of variables : 625 ( 535 ^ 68 !; 21 ?; 625 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: a > a > a ).
thf(func_def_2,type,
cG: a > $o ).
thf(func_def_3,type,
cX: a > $o ).
thf(func_def_4,type,
cR: a > a ).
thf(func_def_5,type,
cL: a > a ).
thf(func_def_6,type,
cF: a > $o ).
thf(func_def_7,type,
cZ: a ).
thf(func_def_24,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
sK2: a ).
thf(func_def_26,type,
sK3: a ).
thf(func_def_27,type,
sK4: a ).
thf(func_def_28,type,
sK5: a > $o ).
thf(func_def_29,type,
sK6: a ).
thf(func_def_30,type,
sK7: a ).
thf(func_def_31,type,
sK8: a ).
thf(func_def_32,type,
sK9: a ).
thf(func_def_33,type,
sK10: a ).
thf(func_def_34,type,
sK11: a ).
thf(func_def_35,type,
sK12: a ).
thf(func_def_36,type,
sK13: a > $o ).
thf(func_def_37,type,
sK14: a > $o ).
thf(func_def_38,type,
sK15: a > a > $o ).
thf(func_def_39,type,
sK16: a ).
thf(func_def_40,type,
sK17: a ).
thf(func_def_41,type,
sK18: a ).
thf(func_def_42,type,
sK19: a ).
thf(func_def_43,type,
sK20: a ).
thf(func_def_44,type,
sK21: a ).
thf(func_def_45,type,
sK22: a > $o ).
thf(func_def_46,type,
sK23: a > $o ).
thf(func_def_47,type,
sK24: a > a > $o ).
thf(func_def_48,type,
sK25: a ).
thf(f1941,plain,
$false,
inference(avatar_sat_refutation,[],[f45,f67,f304,f1045,f1114,f1787,f1940]) ).
thf(f1940,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f1939]) ).
thf(f1939,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f1938]) ).
thf(f1938,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1937]) ).
thf(f1937,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f1935,f1936]) ).
thf(f1936,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( cL @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1934]) ).
thf(f1934,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( cL @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1882,f1932]) ).
thf(f1932,plain,
( ( $true
= ( sK5 @ sK3 ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1882]) ).
thf(f1882,plain,
( ( $true
= ( ( sK5 @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( cL @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1864]) ).
thf(f1864,plain,
( ( ( ( ( sK5 @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( cL @ Y0 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK4 )
& ( sK5 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1861]) ).
thf(f1861,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK4 )
& ( Y0 @ Y1 ) ) ) )
@ sK5 )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(sigma_clausification,[],[f1858]) ).
thf(f1858,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK4 )
& ( Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f1839]) ).
thf(f1839,plain,
( ( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK4 )
& ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1838]) ).
thf(f1838,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK4 )
& ( Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f1808,f1837]) ).
thf(f1837,plain,
( ( ( cX @ sK4 )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1836]) ).
thf(f1836,plain,
( ( ( $true
=> ( cX @ sK4 ) )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1832,f1835]) ).
thf(f1835,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK3 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK4 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1832]) ).
thf(f1832,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK3 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK4 )
& ( Y0 @ Y1 ) ) ) ) )
=> ( cX @ sK4 ) )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1830]) ).
thf(f1830,plain,
( ( ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK3 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) )
@ sK4 )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(sigma_clausification,[],[f1806]) ).
thf(f1806,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK3 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1805]) ).
thf(f1805,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK3 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& $true )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1804]) ).
thf(f1804,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK3 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& ( ( cF @ ( cP @ sK3 @ sK2 ) )
| $true ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f1157,f1800]) ).
thf(f1800,plain,
( ( $true
= ( cG @ ( cP @ sK3 @ sK2 ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1794]) ).
thf(f1794,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& ( cG @ ( cP @ sK3 @ sK2 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1793]) ).
thf(f1793,plain,
( ( $true
= ( ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) )
@ sK3 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f63]) ).
thf(f63,plain,
( ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f62,plain,
( spl0_5
<=> ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f1157,plain,
( ! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& ( ( cF @ ( cP @ X1 @ sK2 ) )
| ( cG @ ( cP @ X1 @ sK2 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1156]) ).
thf(f1156,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( ( cF @ ( cP @ Y0 @ sK2 ) )
| ( cG @ ( cP @ Y0 @ sK2 ) ) ) )
@ X1 )
= $false )
| ~ spl0_1 ),
inference(pi_clausification,[],[f41]) ).
thf(f41,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( ( cF @ ( cP @ Y0 @ sK2 ) )
| ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f40,plain,
( spl0_1
<=> ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( ( cF @ ( cP @ Y0 @ sK2 ) )
| ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f1808,plain,
( ! [X1: a] :
( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= X1 )
& ( Y0 @ Y1 ) ) ) ) )
=> ( cX @ X1 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1807]) ).
thf(f1807,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) )
@ X1 ) )
| ~ spl0_5 ),
inference(pi_clausification,[],[f1803]) ).
thf(f1803,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1802]) ).
thf(f1802,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& $true ) )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1794,f1800]) ).
thf(f1935,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( cL @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1933]) ).
thf(f1933,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( cL @ Y0 ) ) ) )
& $true ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1891,f1932]) ).
thf(f1891,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( cL @ Y0 ) ) ) )
& ( sK5 @ sK3 ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1889]) ).
thf(f1889,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( sK5 @ ( cL @ Y0 ) ) ) )
& ( sK5 @ sK3 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f1841,f1884]) ).
thf(f1884,plain,
( ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK4 )
& ( sK5 @ Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1883]) ).
thf(f1883,plain,
( ( ( $true
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK4 )
& ( sK5 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1864,f1882]) ).
thf(f1841,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X1 @ ( cL @ Y0 ) ) ) )
& ( X1 @ sK3 ) )
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK4 )
& ( X1 @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1840]) ).
thf(f1840,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK3 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK4 )
& ( Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(pi_clausification,[],[f1835]) ).
thf(f1787,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f1786]) ).
thf(f1786,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f1785]) ).
thf(f1785,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1784]) ).
thf(f1784,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1782,f1783]) ).
thf(f1783,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK22 @ Y0 )
=> ( sK22 @ ( cL @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1781]) ).
thf(f1781,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK22 @ Y0 )
=> ( sK22 @ ( cL @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1496,f1779]) ).
thf(f1779,plain,
( ( $true
= ( sK22 @ sK18 ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1496]) ).
thf(f1496,plain,
( ( $true
= ( ( sK22 @ sK18 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK22 @ Y0 )
=> ( sK22 @ ( cL @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1331]) ).
thf(f1331,plain,
( ( $false
= ( ( ( sK22 @ sK18 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK22 @ Y0 )
=> ( sK22 @ ( cL @ Y0 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK20 )
& ( sK22 @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1329]) ).
thf(f1329,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( Y0 @ sK18 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK20 )
& ( Y0 @ Y1 ) ) ) )
@ sK22 )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(sigma_clausification,[],[f1232]) ).
thf(f1232,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK18 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK20 )
& ( Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(not_proxy_clausification,[],[f1197]) ).
thf(f1197,plain,
( ( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK18 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK20 )
& ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1196]) ).
thf(f1196,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK18 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK20 )
& ( Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f1147,f1190]) ).
thf(f1190,plain,
( ( $false
= ( cX @ sK20 ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1177]) ).
thf(f1177,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK18 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK20 )
& ( Y0 @ Y1 ) ) ) ) )
=> ( cX @ sK20 ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1175]) ).
thf(f1175,plain,
( ( ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK18 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) )
@ sK20 )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(sigma_clausification,[],[f1171]) ).
thf(f1171,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK18 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1170]) ).
thf(f1170,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK18 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& $true )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1169]) ).
thf(f1169,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK18 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& ( $true
| ( cG @ ( cP @ sK18 @ sK2 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f1157,f1145]) ).
thf(f1145,plain,
( ( $true
= ( cF @ ( cP @ sK18 @ sK2 ) ) )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1144]) ).
thf(f1144,plain,
( ( $true
= ( $true
& ( cF @ ( cP @ sK18 @ sK2 ) ) ) )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1139,f1143]) ).
thf(f1143,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK18 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1139]) ).
thf(f1139,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK18 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& ( cF @ ( cP @ sK18 @ sK2 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1138]) ).
thf(f1138,plain,
( ( $true
= ( ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) )
@ sK18 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f66]) ).
thf(f66,plain,
( ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f65,plain,
( spl0_6
<=> ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f1147,plain,
( ! [X1: a] :
( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK18 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= X1 )
& ( Y0 @ Y1 ) ) ) ) )
=> ( cX @ X1 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1146]) ).
thf(f1146,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK18 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) )
@ X1 ) )
| ~ spl0_6 ),
inference(pi_clausification,[],[f1143]) ).
thf(f1782,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( sK22 @ Y0 )
=> ( sK22 @ ( cL @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1780]) ).
thf(f1780,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK22 @ Y0 )
=> ( sK22 @ ( cL @ Y0 ) ) ) )
& $true ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1502,f1779]) ).
thf(f1502,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK22 @ Y0 )
=> ( sK22 @ ( cL @ Y0 ) ) ) )
& ( sK22 @ sK18 ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1500]) ).
thf(f1500,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK22 @ Y0 )
=> ( sK22 @ ( cL @ Y0 ) ) ) )
& ( sK22 @ sK18 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f1199,f1498]) ).
thf(f1498,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK20 )
& ( sK22 @ Y0 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1497]) ).
thf(f1497,plain,
( ( ( $true
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK20 )
& ( sK22 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1331,f1496]) ).
thf(f1199,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X1 @ ( cL @ Y0 ) ) ) )
& ( X1 @ sK18 ) )
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK20 )
& ( X1 @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1198]) ).
thf(f1198,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK18 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK20 )
& ( Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(pi_clausification,[],[f1191]) ).
thf(f1191,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK18 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK20 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1177]) ).
thf(f1114,plain,
( ~ spl0_2
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1113]) ).
thf(f1113,plain,
( $false
| ~ spl0_2
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f1112]) ).
thf(f1112,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1111]) ).
thf(f1111,plain,
( ( $true = ~ $true )
| ~ spl0_2
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1110,f1109]) ).
thf(f1109,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1108]) ).
thf(f1108,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) )
& $true ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1088,f1105]) ).
thf(f1105,plain,
( ( $true
= ( sK15 @ sK9 @ sK7 ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1088]) ).
thf(f1088,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) )
& ( sK15 @ sK9 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1085]) ).
thf(f1085,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) )
& ( sK15 @ sK9 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK9 )
& ( sK15 @ sK9 @ Y0 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f1083]) ).
thf(f1083,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) )
@ ( sK15 @ sK9 ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(sigma_clausification,[],[f1080]) ).
thf(f1080,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(not_proxy_clausification,[],[f1061]) ).
thf(f1061,plain,
( ( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1060]) ).
thf(f1060,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f295,f1059]) ).
thf(f1059,plain,
( ( ( cX @ sK9 )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1058]) ).
thf(f1058,plain,
( ( ( $true
=> ( cX @ sK9 ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1055,f1057]) ).
thf(f1057,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1055]) ).
thf(f1055,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) )
=> ( cX @ sK9 ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f1050]) ).
thf(f1050,plain,
( ( $false
= ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) )
@ sK9 ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(sigma_clausification,[],[f1049]) ).
thf(f1049,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1048]) ).
thf(f1048,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& $true )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f351,f300]) ).
thf(f300,plain,
( ( $true
= ( cF @ ( cP @ sK7 @ sK2 ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f299]) ).
thf(f299,plain,
( spl0_13
<=> ( $true
= ( cF @ ( cP @ sK7 @ sK2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f351,plain,
( ! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& ( cF @ ( cP @ X1 @ sK2 ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f350]) ).
thf(f350,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) )
@ X1 )
= $false )
| ~ spl0_2 ),
inference(pi_clausification,[],[f333]) ).
thf(f333,plain,
( ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
( ( ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f43,plain,
( spl0_2
<=> ( ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f295,plain,
( ! [X1: a] :
( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= X1 )
& ( Y0 @ Y1 ) ) ) ) )
=> ( cX @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f294]) ).
thf(f294,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f293]) ).
thf(f293,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f292]) ).
thf(f292,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f283,f290]) ).
thf(f290,plain,
( ( $true
= ( ( cF @ ( cP @ sK7 @ sK2 ) )
| ( cG @ ( cP @ sK7 @ sK2 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f283]) ).
thf(f283,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& ( ( cF @ ( cP @ sK7 @ sK2 ) )
| ( cG @ ( cP @ sK7 @ sK2 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f282]) ).
thf(f282,plain,
( ( $true
= ( ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( ( cF @ ( cP @ Y0 @ sK2 ) )
| ( cG @ ( cP @ Y0 @ sK2 ) ) ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f279]) ).
thf(f279,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( ( cF @ ( cP @ Y0 @ sK2 ) )
| ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
!= $false )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f31,f44]) ).
thf(f31,plain,
( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( ( cF @ ( cP @ Y0 @ sK2 ) )
| ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
!= ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f30]) ).
thf(f30,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( ( cF @ ( cP @ Y1 @ Y0 ) )
| ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cF @ ( cP @ Y1 @ Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f27]) ).
thf(f27,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( ( cF @ ( cP @ Y1 @ Y0 ) )
| ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cF @ ( cP @ Y1 @ Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f10]) ).
thf(f10,plain,
( ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( ( cF @ ( cP @ Y1 @ Y0 ) )
| ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cF @ ( cP @ Y1 @ Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( cL @ Y2 ) ) ) ) ) )
=> ( Y0 @ cZ ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y0 @ Y1 ) )
= Y0 ) ) )
& ( cZ
= ( cL @ cZ ) ) )
=> ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( ( cF @ ( cP @ Y1 @ Y0 ) )
| ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cF @ ( cP @ Y1 @ Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( cL @ Y2 ) ) ) ) ) )
=> ( Y0 @ cZ ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y0 @ Y1 ) )
= Y0 ) ) )
& ( cZ
= ( cL @ cZ ) ) )
=> ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( ( cF @ ( cP @ Y1 @ Y0 ) )
| ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cF @ ( cP @ Y1 @ Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( cL @ Y2 ) ) ) ) ) )
=> ( Y0 @ cZ ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y0 @ Y1 ) )
= Y0 ) ) )
& ( cZ
= ( cL @ cZ ) ) )
=> ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( ( cF @ ( cP @ Y1 @ Y0 ) )
| ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cF @ ( cP @ Y1 @ Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
=> ( cX @ Y2 ) ) )
& ( cG @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ( ( cZ
= ( cL @ cZ ) )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X1 @ X0 ) )
= X1 )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a,X3: a] :
( ( cR @ ( cP @ X2 @ X3 ) )
= X3 )
& ! [X4: a > $o] :
( ? [X5: a] :
( ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( cL @ X6 ) ) )
& ( X4 @ X5 ) )
=> ( X4 @ cZ ) )
& ! [X7: a] :
( ( cZ != X7 )
<=> ( ( cP @ ( cL @ X7 ) @ ( cR @ X7 ) )
= X7 ) ) )
=> ( ( ^ [X8: a] :
? [X9: a] :
( ( ( cG @ ( cP @ X9 @ X8 ) )
| ( cF @ ( cP @ X9 @ X8 ) ) )
& ! [X10: a] :
( ! [X11: a > $o] :
( ( ( X11 @ X9 )
& ! [X12: a] :
( ( X11 @ X12 )
=> ( X11 @ ( cL @ X12 ) ) ) )
=> ? [X13: a] :
( ( X11 @ X13 )
& ( ( cR @ X13 )
= X10 ) ) )
=> ( cX @ X10 ) ) ) )
= ( ^ [X14: a] :
( ? [X15: a] :
( ( cG @ ( cP @ X15 @ X14 ) )
& ! [X16: a] :
( ! [X17: a > $o] :
( ( ! [X18: a] :
( ( X17 @ X18 )
=> ( X17 @ ( cL @ X18 ) ) )
& ( X17 @ X15 ) )
=> ? [X19: a] :
( ( X17 @ X19 )
& ( ( cR @ X19 )
= X16 ) ) )
=> ( cX @ X16 ) ) )
| ? [X20: a] :
( ( cF @ ( cP @ X20 @ X14 ) )
& ! [X21: a] :
( ! [X22: a > $o] :
( ( ! [X23: a] :
( ( X22 @ X23 )
=> ( X22 @ ( cL @ X23 ) ) )
& ( X22 @ X20 ) )
=> ? [X24: a] :
( ( X22 @ X24 )
& ( ( cR @ X24 )
= X21 ) ) )
=> ( cX @ X21 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cZ
= ( cL @ cZ ) )
& ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X3: a > $o] :
( ? [X2: a] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) )
& ( X3 @ X2 ) )
=> ( X3 @ cZ ) )
& ! [X2: a] :
( ( cZ != X2 )
<=> ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 ) ) )
=> ( ( ^ [X1: a] :
? [X0: a] :
( ( ( cG @ ( cP @ X0 @ X1 ) )
| ( cF @ ( cP @ X0 @ X1 ) ) )
& ! [X5: a] :
( ! [X3: a > $o] :
( ( ( X3 @ X0 )
& ! [X6: a] :
( ( X3 @ X6 )
=> ( X3 @ ( cL @ X6 ) ) ) )
=> ? [X7: a] :
( ( X3 @ X7 )
& ( ( cR @ X7 )
= X5 ) ) )
=> ( cX @ X5 ) ) ) )
= ( ^ [X6: a] :
( ? [X0: a] :
( ( cG @ ( cP @ X0 @ X6 ) )
& ! [X10: a] :
( ! [X3: a > $o] :
( ( ! [X9: a] :
( ( X3 @ X9 )
=> ( X3 @ ( cL @ X9 ) ) )
& ( X3 @ X0 ) )
=> ? [X7: a] :
( ( X3 @ X7 )
& ( ( cR @ X7 )
= X10 ) ) )
=> ( cX @ X10 ) ) )
| ? [X0: a] :
( ( cF @ ( cP @ X0 @ X6 ) )
& ! [X8: a] :
( ! [X3: a > $o] :
( ( ! [X9: a] :
( ( X3 @ X9 )
=> ( X3 @ ( cL @ X9 ) ) )
& ( X3 @ X0 ) )
=> ? [X7: a] :
( ( X3 @ X7 )
& ( ( cR @ X7 )
= X8 ) ) )
=> ( cX @ X8 ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ( cZ
= ( cL @ cZ ) )
& ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X3: a > $o] :
( ? [X2: a] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) )
& ( X3 @ X2 ) )
=> ( X3 @ cZ ) )
& ! [X2: a] :
( ( cZ != X2 )
<=> ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 ) ) )
=> ( ( ^ [X1: a] :
? [X0: a] :
( ( ( cG @ ( cP @ X0 @ X1 ) )
| ( cF @ ( cP @ X0 @ X1 ) ) )
& ! [X5: a] :
( ! [X3: a > $o] :
( ( ( X3 @ X0 )
& ! [X6: a] :
( ( X3 @ X6 )
=> ( X3 @ ( cL @ X6 ) ) ) )
=> ? [X7: a] :
( ( X3 @ X7 )
& ( ( cR @ X7 )
= X5 ) ) )
=> ( cX @ X5 ) ) ) )
= ( ^ [X6: a] :
( ? [X0: a] :
( ( cG @ ( cP @ X0 @ X6 ) )
& ! [X10: a] :
( ! [X3: a > $o] :
( ( ! [X9: a] :
( ( X3 @ X9 )
=> ( X3 @ ( cL @ X9 ) ) )
& ( X3 @ X0 ) )
=> ? [X7: a] :
( ( X3 @ X7 )
& ( ( cR @ X7 )
= X10 ) ) )
=> ( cX @ X10 ) ) )
| ? [X0: a] :
( ( cF @ ( cP @ X0 @ X6 ) )
& ! [X8: a] :
( ! [X3: a > $o] :
( ( ! [X9: a] :
( ( X3 @ X9 )
=> ( X3 @ ( cL @ X9 ) ) )
& ( X3 @ X0 ) )
=> ? [X7: a] :
( ( X3 @ X7 )
& ( ( cR @ X7 )
= X8 ) ) )
=> ( cX @ X8 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPU_X2310A_pme) ).
thf(f1110,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1107]) ).
thf(f1107,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1095,f1105]) ).
thf(f1095,plain,
( ( $true
= ( ~ ( ( sK15 @ sK9 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1094]) ).
thf(f1094,plain,
( ( $true
= ( ( ( sK15 @ sK9 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f1063,f1087]) ).
thf(f1087,plain,
( ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK9 )
& ( sK15 @ sK9 @ Y0 ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1085]) ).
thf(f1063,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( X1 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X1 @ ( cL @ Y0 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK9 )
& ( X1 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f1062]) ).
thf(f1062,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( Y0 @ sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(pi_clausification,[],[f1057]) ).
thf(f1045,plain,
( ~ spl0_2
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1044]) ).
thf(f1044,plain,
( $false
| ~ spl0_2
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f1043]) ).
thf(f1043,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1042]) ).
thf(f1042,plain,
( ( $true = ~ $true )
| ~ spl0_2
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1040,f1041]) ).
thf(f1041,plain,
( ( $true
= ( sK15 @ sK9 @ sK7 ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1039]) ).
thf(f1039,plain,
( ( $true
= ( $true
& ( sK15 @ sK9 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(backward_demodulation,[],[f979,f1034]) ).
thf(f1034,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f979]) ).
thf(f979,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) )
& ( sK15 @ sK9 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f976]) ).
thf(f976,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) )
& ( sK15 @ sK9 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK9 )
& ( sK15 @ sK9 @ Y0 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f974]) ).
thf(f974,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) )
@ ( sK15 @ sK9 ) )
= $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(sigma_clausification,[],[f971]) ).
thf(f971,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(not_proxy_clausification,[],[f951]) ).
thf(f951,plain,
( ( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(boolean_simplification,[],[f950]) ).
thf(f950,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) )
& ( Y0 @ sK7 ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f295,f949]) ).
thf(f949,plain,
( ( ( cX @ sK9 )
= $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(boolean_simplification,[],[f948]) ).
thf(f948,plain,
( ( ( $true
=> ( cX @ sK9 ) )
= $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(backward_demodulation,[],[f812,f947]) ).
thf(f947,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f812]) ).
thf(f812,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) ) )
=> ( cX @ sK9 ) )
= $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f808]) ).
thf(f808,plain,
( ( $false
= ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) )
@ sK9 ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(sigma_clausification,[],[f807]) ).
thf(f807,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(boolean_simplification,[],[f806]) ).
thf(f806,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK7 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& $true )
= $false )
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f339,f303]) ).
thf(f303,plain,
( ( $true
= ( cG @ ( cP @ sK7 @ sK2 ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f302,plain,
( spl0_14
<=> ( $true
= ( cG @ ( cP @ sK7 @ sK2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f339,plain,
( ! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
=> ( cX @ Y0 ) ) )
& ( cG @ ( cP @ X1 @ sK2 ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f338]) ).
thf(f338,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) )
@ X1 )
= $false )
| ~ spl0_2 ),
inference(pi_clausification,[],[f335]) ).
thf(f335,plain,
( ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f334]) ).
thf(f334,plain,
( ( ( $false
| ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f44,f333]) ).
thf(f1040,plain,
( ( $true
= ( ~ ( sK15 @ sK9 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1038]) ).
thf(f1038,plain,
( ( $true
= ( ~ ( ( sK15 @ sK9 @ sK7 )
& $true ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(backward_demodulation,[],[f985,f1034]) ).
thf(f985,plain,
( ( $true
= ( ~ ( ( sK15 @ sK9 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(boolean_simplification,[],[f983]) ).
thf(f983,plain,
( ( $true
= ( ( ( sK15 @ sK9 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK9 @ Y0 )
=> ( sK15 @ sK9 @ ( cL @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f953,f981]) ).
thf(f981,plain,
( ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK9 )
& ( sK15 @ sK9 @ Y0 ) ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(boolean_simplification,[],[f980]) ).
thf(f980,plain,
( ( $false
= ( $true
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK9 )
& ( sK15 @ sK9 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(backward_demodulation,[],[f976,f979]) ).
thf(f953,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( X1 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X1 @ ( cL @ Y0 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y0: a] :
( ( ( cR @ Y0 )
= sK9 )
& ( X1 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f952]) ).
thf(f952,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( Y0 @ sK7 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cL @ Y1 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y1: a] :
( ( ( cR @ Y1 )
= sK9 )
& ( Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_14 ),
inference(pi_clausification,[],[f947]) ).
thf(f304,plain,
( spl0_13
| spl0_14
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f297,f43,f302,f299]) ).
thf(f297,plain,
( ( $true
= ( cG @ ( cP @ sK7 @ sK2 ) ) )
| ( $true
= ( cF @ ( cP @ sK7 @ sK2 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f290]) ).
thf(f67,plain,
( spl0_5
| spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f60,f40,f65,f62]) ).
thf(f60,plain,
( ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
| ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f57]) ).
thf(f57,plain,
( ( ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
!= $false )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f31,f41]) ).
thf(f45,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f38,f43,f40]) ).
thf(f38,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( ( cF @ ( cP @ Y0 @ sK2 ) )
| ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
= $false )
| ( ( ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cF @ ( cP @ Y0 @ sK2 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
=> ( cX @ Y1 ) ) )
& ( cG @ ( cP @ Y0 @ sK2 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG290^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 23:40:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (25029)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)
% 0.14/0.37 % (25030)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)
% 0.14/0.37 % (25029)Instruction limit reached!
% 0.14/0.37 % (25029)------------------------------
% 0.14/0.37 % (25029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (25029)Termination reason: Unknown
% 0.14/0.37 % (25029)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (25029)Memory used [KB]: 1023
% 0.14/0.37 % (25029)Time elapsed: 0.004 s
% 0.14/0.37 % (25029)Instructions burned: 4 (million)
% 0.14/0.37 % (25029)------------------------------
% 0.14/0.37 % (25029)------------------------------
% 0.14/0.38 % (25028)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (25031)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (25032)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)
% 0.14/0.38 % (25034)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (25035)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)
% 0.14/0.39 % (25031)Instruction limit reached!
% 0.14/0.39 % (25031)------------------------------
% 0.14/0.39 % (25031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (25031)Termination reason: Unknown
% 0.14/0.39 % (25031)Termination phase: Property scanning
% 0.14/0.39 % (25032)Instruction limit reached!
% 0.14/0.39 % (25032)------------------------------
% 0.14/0.39 % (25032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (25032)Termination reason: Unknown
% 0.14/0.39 % (25032)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (25032)Memory used [KB]: 1023
% 0.14/0.39 % (25032)Time elapsed: 0.005 s
% 0.14/0.39 % (25032)Instructions burned: 2 (million)
% 0.14/0.39 % (25032)------------------------------
% 0.14/0.39 % (25032)------------------------------
% 0.14/0.39
% 0.14/0.39 % (25031)Memory used [KB]: 1023
% 0.14/0.39 % (25031)Time elapsed: 0.005 s
% 0.14/0.39 % (25031)Instructions burned: 2 (million)
% 0.14/0.39 % (25031)------------------------------
% 0.14/0.39 % (25031)------------------------------
% 0.14/0.39 % (25035)Instruction limit reached!
% 0.14/0.39 % (25035)------------------------------
% 0.14/0.39 % (25035)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (25035)Termination reason: Unknown
% 0.14/0.39 % (25035)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (25035)Memory used [KB]: 1023
% 0.14/0.39 % (25035)Time elapsed: 0.005 s
% 0.14/0.39 % (25035)Instructions burned: 3 (million)
% 0.14/0.39 % (25035)------------------------------
% 0.14/0.39 % (25035)------------------------------
% 0.14/0.39 % (25036)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)
% 0.14/0.39 % (25030)Instruction limit reached!
% 0.14/0.39 % (25030)------------------------------
% 0.14/0.39 % (25030)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (25030)Termination reason: Unknown
% 0.14/0.39 % (25030)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (25030)Memory used [KB]: 5628
% 0.14/0.39 % (25030)Time elapsed: 0.017 s
% 0.14/0.39 % (25030)Instructions burned: 28 (million)
% 0.14/0.39 % (25030)------------------------------
% 0.14/0.39 % (25030)------------------------------
% 0.22/0.39 % (25033)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)
% 0.22/0.40 % (25034)Instruction limit reached!
% 0.22/0.40 % (25034)------------------------------
% 0.22/0.40 % (25034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (25034)Termination reason: Unknown
% 0.22/0.40 % (25034)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (25034)Memory used [KB]: 5628
% 0.22/0.40 % (25034)Time elapsed: 0.021 s
% 0.22/0.40 % (25034)Instructions burned: 18 (million)
% 0.22/0.40 % (25034)------------------------------
% 0.22/0.40 % (25034)------------------------------
% 0.22/0.41 % (25038)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.41 % (25037)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)
% 0.22/0.41 % (25040)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.41 % (25038)Instruction limit reached!
% 0.22/0.41 % (25038)------------------------------
% 0.22/0.41 % (25038)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (25038)Termination reason: Unknown
% 0.22/0.41 % (25038)Termination phase: Preprocessing 1
% 0.22/0.41
% 0.22/0.41 % (25038)Memory used [KB]: 1023
% 0.22/0.41 % (25038)Time elapsed: 0.005 s
% 0.22/0.41 % (25038)Instructions burned: 3 (million)
% 0.22/0.41 % (25039)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 theBenchmark for (2999ds/1041Mi)
% 0.22/0.41 % (25038)------------------------------
% 0.22/0.41 % (25038)------------------------------
% 0.22/0.42 % (25040)Instruction limit reached!
% 0.22/0.42 % (25040)------------------------------
% 0.22/0.42 % (25040)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (25040)Termination reason: Unknown
% 0.22/0.42 % (25040)Termination phase: Saturation
% 0.22/0.42 % (25041)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.42
% 0.22/0.42 % (25040)Memory used [KB]: 1023
% 0.22/0.42 % (25040)Time elapsed: 0.010 s
% 0.22/0.42 % (25040)Instructions burned: 7 (million)
% 0.22/0.42 % (25040)------------------------------
% 0.22/0.42 % (25040)------------------------------
% 0.22/0.42 % (25036)Instruction limit reached!
% 0.22/0.42 % (25036)------------------------------
% 0.22/0.42 % (25036)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (25036)Termination reason: Unknown
% 0.22/0.42 % (25036)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (25036)Memory used [KB]: 5628
% 0.22/0.42 % (25036)Time elapsed: 0.033 s
% 0.22/0.42 % (25036)Instructions burned: 37 (million)
% 0.22/0.42 % (25036)------------------------------
% 0.22/0.42 % (25036)------------------------------
% 0.22/0.43 % (25037)Instruction limit reached!
% 0.22/0.43 % (25037)------------------------------
% 0.22/0.43 % (25037)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (25037)Termination reason: Unknown
% 0.22/0.43 % (25037)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (25037)Memory used [KB]: 5756
% 0.22/0.43 % (25037)Time elapsed: 0.018 s
% 0.22/0.43 % (25037)Instructions burned: 16 (million)
% 0.22/0.43 % (25037)------------------------------
% 0.22/0.43 % (25037)------------------------------
% 0.22/0.43 % (25041)Instruction limit reached!
% 0.22/0.43 % (25041)------------------------------
% 0.22/0.43 % (25041)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (25041)Termination reason: Unknown
% 0.22/0.43 % (25041)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (25041)Memory used [KB]: 5884
% 0.22/0.43 % (25041)Time elapsed: 0.012 s
% 0.22/0.43 % (25041)Instructions burned: 16 (million)
% 0.22/0.43 % (25041)------------------------------
% 0.22/0.43 % (25041)------------------------------
% 0.22/0.44 % (25042)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 theBenchmark for (2999ds/3Mi)
% 0.22/0.44 % (25042)Instruction limit reached!
% 0.22/0.44 % (25042)------------------------------
% 0.22/0.44 % (25042)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (25042)Termination reason: Unknown
% 0.22/0.44 % (25042)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (25042)Memory used [KB]: 1023
% 0.22/0.44 % (25042)Time elapsed: 0.004 s
% 0.22/0.44 % (25042)Instructions burned: 3 (million)
% 0.22/0.44 % (25042)------------------------------
% 0.22/0.44 % (25042)------------------------------
% 0.22/0.44 % (25043)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 theBenchmark for (2999ds/3Mi)
% 0.22/0.44 % (25046)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.44 % (25043)Instruction limit reached!
% 0.22/0.44 % (25043)------------------------------
% 0.22/0.44 % (25043)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (25043)Termination reason: Unknown
% 0.22/0.44 % (25043)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (25043)Memory used [KB]: 1023
% 0.22/0.44 % (25043)Time elapsed: 0.004 s
% 0.22/0.44 % (25043)Instructions burned: 3 (million)
% 0.22/0.44 % (25043)------------------------------
% 0.22/0.44 % (25043)------------------------------
% 0.22/0.44 % (25044)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.44 % (25045)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.45 % (25046)Instruction limit reached!
% 0.22/0.45 % (25046)------------------------------
% 0.22/0.45 % (25046)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (25046)Termination reason: Unknown
% 0.22/0.45 % (25046)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (25046)Memory used [KB]: 5500
% 0.22/0.45 % (25046)Time elapsed: 0.004 s
% 0.22/0.45 % (25046)Instructions burned: 5 (million)
% 0.22/0.45 % (25046)------------------------------
% 0.22/0.45 % (25046)------------------------------
% 0.22/0.45 % (25045)Instruction limit reached!
% 0.22/0.45 % (25045)------------------------------
% 0.22/0.45 % (25045)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (25045)Termination reason: Unknown
% 0.22/0.45 % (25045)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (25045)Memory used [KB]: 1023
% 0.22/0.45 % (25045)Time elapsed: 0.003 s
% 0.22/0.45 % (25045)Instructions burned: 3 (million)
% 0.22/0.45 % (25045)------------------------------
% 0.22/0.45 % (25045)------------------------------
% 0.22/0.45 % (25044)Instruction limit reached!
% 0.22/0.45 % (25044)------------------------------
% 0.22/0.45 % (25044)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (25044)Termination reason: Unknown
% 0.22/0.45 % (25044)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (25044)Memory used [KB]: 5500
% 0.22/0.45 % (25044)Time elapsed: 0.008 s
% 0.22/0.45 % (25044)Instructions burned: 7 (million)
% 0.22/0.45 % (25044)------------------------------
% 0.22/0.45 % (25044)------------------------------
% 0.22/0.45 % (25047)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.46 % (25048)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.46 % (25049)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.46 % (25050)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 theBenchmark for (2999ds/902Mi)
% 0.22/0.46 % (25049)Instruction limit reached!
% 0.22/0.46 % (25049)------------------------------
% 0.22/0.46 % (25049)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (25049)Termination reason: Unknown
% 0.22/0.46 % (25049)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (25049)Memory used [KB]: 5500
% 0.22/0.46 % (25049)Time elapsed: 0.005 s
% 0.22/0.46 % (25049)Instructions burned: 6 (million)
% 0.22/0.46 % (25049)------------------------------
% 0.22/0.46 % (25049)------------------------------
% 0.22/0.46 % (25047)Instruction limit reached!
% 0.22/0.46 % (25047)------------------------------
% 0.22/0.46 % (25047)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (25047)Termination reason: Unknown
% 0.22/0.46 % (25047)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (25047)Memory used [KB]: 5628
% 0.22/0.46 % (25047)Time elapsed: 0.012 s
% 0.22/0.46 % (25047)Instructions burned: 19 (million)
% 0.22/0.46 % (25047)------------------------------
% 0.22/0.46 % (25047)------------------------------
% 0.22/0.47 % (25051)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 theBenchmark for (2999ds/21Mi)
% 0.22/0.48 % (25052)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.48 % (25053)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 theBenchmark for (2999ds/6Mi)
% 0.22/0.48 % (25051)Instruction limit reached!
% 0.22/0.48 % (25051)------------------------------
% 0.22/0.48 % (25051)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (25051)Termination reason: Unknown
% 0.22/0.48 % (25051)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (25051)Memory used [KB]: 5628
% 0.22/0.48 % (25051)Time elapsed: 0.015 s
% 0.22/0.48 % (25051)Instructions burned: 21 (million)
% 0.22/0.48 % (25051)------------------------------
% 0.22/0.48 % (25051)------------------------------
% 0.22/0.48 % (25052)Instruction limit reached!
% 0.22/0.48 % (25052)------------------------------
% 0.22/0.48 % (25052)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (25052)Termination reason: Unknown
% 0.22/0.48 % (25052)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (25052)Memory used [KB]: 5500
% 0.22/0.48 % (25052)Time elapsed: 0.005 s
% 0.22/0.48 % (25052)Instructions burned: 6 (million)
% 0.22/0.48 % (25052)------------------------------
% 0.22/0.48 % (25052)------------------------------
% 0.22/0.48 % (25053)Instruction limit reached!
% 0.22/0.48 % (25053)------------------------------
% 0.22/0.48 % (25053)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (25053)Termination reason: Unknown
% 0.22/0.48 % (25053)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (25053)Memory used [KB]: 5500
% 0.22/0.48 % (25053)Time elapsed: 0.005 s
% 0.22/0.48 % (25053)Instructions burned: 7 (million)
% 0.22/0.48 % (25053)------------------------------
% 0.22/0.48 % (25053)------------------------------
% 0.22/0.49 % (25054)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.22/0.50 % (25055)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 theBenchmark for (2998ds/779Mi)
% 0.22/0.50 % (25056)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 theBenchmark for (2998ds/19Mi)
% 0.22/0.51 % (25056)Instruction limit reached!
% 0.22/0.51 % (25056)------------------------------
% 0.22/0.51 % (25056)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (25056)Termination reason: Unknown
% 0.22/0.51 % (25056)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (25056)Memory used [KB]: 5500
% 0.22/0.51 % (25056)Time elapsed: 0.012 s
% 0.22/0.51 % (25056)Instructions burned: 19 (million)
% 0.22/0.51 % (25056)------------------------------
% 0.22/0.51 % (25056)------------------------------
% 0.22/0.51 % (25028)Instruction limit reached!
% 0.22/0.51 % (25028)------------------------------
% 0.22/0.51 % (25028)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (25028)Termination reason: Unknown
% 0.22/0.51 % (25028)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (25028)Memory used [KB]: 6652
% 0.22/0.51 % (25028)Time elapsed: 0.132 s
% 0.22/0.51 % (25028)Instructions burned: 183 (million)
% 0.22/0.51 % (25028)------------------------------
% 0.22/0.51 % (25028)------------------------------
% 0.22/0.52 % (25057)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 1.37/0.53 % (25058)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 1.37/0.54 % (25058)Instruction limit reached!
% 1.37/0.54 % (25058)------------------------------
% 1.37/0.54 % (25058)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.37/0.54 % (25058)Termination reason: Unknown
% 1.37/0.54 % (25058)Termination phase: Saturation
% 1.37/0.54
% 1.37/0.54 % (25058)Memory used [KB]: 5756
% 1.37/0.54 % (25058)Time elapsed: 0.013 s
% 1.37/0.54 % (25058)Instructions burned: 17 (million)
% 1.37/0.54 % (25058)------------------------------
% 1.37/0.54 % (25058)------------------------------
% 1.55/0.55 % (25059)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 1.55/0.55 % (25059)Instruction limit reached!
% 1.55/0.55 % (25059)------------------------------
% 1.55/0.55 % (25059)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.55/0.55 % (25059)Termination reason: Unknown
% 1.55/0.55 % (25059)Termination phase: Preprocessing 3
% 1.55/0.55
% 1.55/0.55 % (25059)Memory used [KB]: 1023
% 1.55/0.55 % (25059)Time elapsed: 0.004 s
% 1.55/0.55 % (25059)Instructions burned: 4 (million)
% 1.55/0.55 % (25059)------------------------------
% 1.55/0.55 % (25059)------------------------------
% 1.55/0.57 % (25060)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 1.55/0.59 % (25060)Instruction limit reached!
% 1.55/0.59 % (25060)------------------------------
% 1.55/0.59 % (25060)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.55/0.59 % (25060)Termination reason: Unknown
% 1.55/0.59 % (25060)Termination phase: Saturation
% 1.55/0.59
% 1.55/0.59 % (25060)Memory used [KB]: 5756
% 1.55/0.59 % (25060)Time elapsed: 0.043 s
% 1.55/0.59 % (25060)Instructions burned: 31 (million)
% 1.55/0.59 % (25060)------------------------------
% 1.55/0.59 % (25060)------------------------------
% 1.55/0.59 % (25033)Instruction limit reached!
% 1.55/0.59 % (25033)------------------------------
% 1.55/0.59 % (25033)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.55/0.59 % (25033)Termination reason: Unknown
% 1.55/0.59 % (25033)Termination phase: Saturation
% 1.55/0.59
% 1.55/0.59 % (25033)Memory used [KB]: 7036
% 1.55/0.59 % (25033)Time elapsed: 0.212 s
% 1.55/0.59 % (25033)Instructions burned: 275 (million)
% 1.55/0.59 % (25033)------------------------------
% 1.55/0.59 % (25033)------------------------------
% 1.55/0.60 % (25061)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2997ds/127Mi)
% 1.55/0.61 % (25062)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2997ds/100Mi)
% 2.14/0.65 % (25039)First to succeed.
% 2.14/0.66 % (25039)Refutation found. Thanks to Tanya!
% 2.14/0.66 % SZS status Theorem for theBenchmark
% 2.14/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.14/0.66 % (25039)------------------------------
% 2.14/0.66 % (25039)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.14/0.66 % (25039)Termination reason: Refutation
% 2.14/0.66
% 2.14/0.66 % (25039)Memory used [KB]: 6652
% 2.14/0.66 % (25039)Time elapsed: 0.246 s
% 2.14/0.66 % (25039)Instructions burned: 358 (million)
% 2.14/0.66 % (25039)------------------------------
% 2.14/0.66 % (25039)------------------------------
% 2.14/0.66 % (25027)Success in time 0.306 s
% 2.14/0.66 % Vampire---4.8 exiting
%------------------------------------------------------------------------------