TSTP Solution File: NUM783_8 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM783_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 : Tue May 21 02:13:24 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 45
% Syntax : Number of formulae : 205 ( 9 unt; 17 typ; 0 def)
% Number of atoms : 894 ( 90 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 569 ( 254 ~; 278 |; 6 &)
% ( 28 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 393 ( 391 fml; 2 var)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 11 >; 13 *; 0 +; 0 <<)
% Number of predicates : 33 ( 30 usr; 21 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 61 ( 61 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
rat: $tType ).
tff(func_def_0,type,
x0: rat ).
tff(func_def_1,type,
y0: rat ).
tff(func_def_4,type,
bG0: $o ).
tff(func_def_5,type,
bG1: $o ).
tff(func_def_6,type,
bG2: $o ).
tff(func_def_7,type,
bG3: ( rat * rat ) > $o ).
tff(func_def_8,type,
bG4: ( rat * rat ) > $o ).
tff(func_def_9,type,
bG5: ( rat * rat ) > $o ).
tff(func_def_10,type,
bG6: ( rat * rat ) > $o ).
tff(func_def_11,type,
bG7: ( rat * rat ) > $o ).
tff(func_def_12,type,
bG8: ( rat * rat ) > $o ).
tff(pred_def_1,type,
or3: ( $o * $o * $o ) > $o ).
tff(pred_def_2,type,
is: ( rat * rat ) > $o ).
tff(pred_def_3,type,
more: ( rat * rat ) > $o ).
tff(pred_def_4,type,
less: ( rat * rat ) > $o ).
tff(pred_def_5,type,
ec3: ( $o * $o * $o ) > $o ).
tff(f457,plain,
$false,
inference(avatar_sat_refutation,[],[f71,f72,f81,f82,f91,f92,f113,f123,f194,f200,f215,f233,f244,f251,f256,f264,f315,f332,f347,f388,f403,f410,f417,f418,f422,f425,f438,f456]) ).
tff(f456,plain,
( ~ spl9_2
| ~ spl9_6
| ~ spl9_13
| spl9_15 ),
inference(avatar_contradiction_clause,[],[f455]) ).
tff(f455,plain,
( $false
| ~ spl9_2
| ~ spl9_6
| ~ spl9_13
| spl9_15 ),
inference(subsumption_resolution,[],[f454,f208]) ).
tff(f208,plain,
( ~ or3($true,$false,$true)
| spl9_15 ),
inference(avatar_component_clause,[],[f206]) ).
tff(f206,plain,
( spl9_15
<=> or3($true,$false,$true) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
tff(f454,plain,
( or3($true,$false,$true)
| ~ spl9_2
| ~ spl9_6
| ~ spl9_13 ),
inference(forward_demodulation,[],[f453,f426]) ).
tff(f426,plain,
( ( $true = bG3(y0,x0) )
| ~ spl9_6 ),
inference(resolution,[],[f90,f51]) ).
tff(f51,plain,
! [X0: rat,X1: rat] :
( ~ is(X1,X0)
| ( $true = bG3(X0,X1) ) ),
inference(cnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: rat,X1: rat] :
( ( is(X1,X0)
| ( $true != bG3(X0,X1) ) )
& ( ( $true = bG3(X0,X1) )
| ~ is(X1,X0) ) ),
inference(nnf_transformation,[],[f26]) ).
tff(f26,plain,
! [X0: rat,X1: rat] :
( is(X1,X0)
<=> ( $true = bG3(X0,X1) ) ),
inference(rectify,[],[f14]) ).
tff(f14,plain,
! [X1: rat,X0: rat] :
( is(X0,X1)
<=> ( $true = bG3(X1,X0) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG3])]) ).
tff(f90,plain,
( is(x0,y0)
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f88,plain,
( spl9_6
<=> is(x0,y0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
tff(f453,plain,
( or3(bG3(y0,x0),$false,$true)
| ~ spl9_2
| ~ spl9_13 ),
inference(forward_demodulation,[],[f450,f356]) ).
tff(f356,plain,
( ( $true = bG5(y0,x0) )
| ~ spl9_2 ),
inference(resolution,[],[f70,f47]) ).
tff(f47,plain,
! [X0: rat,X1: rat] :
( ~ less(X1,X0)
| ( $true = bG5(X0,X1) ) ),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: rat,X1: rat] :
( ( less(X1,X0)
| ( $true != bG5(X0,X1) ) )
& ( ( $true = bG5(X0,X1) )
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,plain,
! [X0: rat,X1: rat] :
( less(X1,X0)
<=> ( $true = bG5(X0,X1) ) ),
inference(rectify,[],[f16]) ).
tff(f16,plain,
! [X1: rat,X0: rat] :
( less(X0,X1)
<=> ( $true = bG5(X1,X0) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG5])]) ).
tff(f70,plain,
( less(x0,y0)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f68]) ).
tff(f68,plain,
( spl9_2
<=> less(x0,y0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
tff(f450,plain,
( or3(bG3(y0,x0),$false,bG5(y0,x0))
| ~ spl9_13 ),
inference(superposition,[],[f61,f189]) ).
tff(f189,plain,
( ( $false = bG4(y0,x0) )
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f187]) ).
tff(f187,plain,
( spl9_13
<=> ( $false = bG4(y0,x0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
tff(f61,plain,
! [X0: rat,X1: rat] : or3(bG3(X1,X0),bG4(X1,X0),bG5(X1,X0)),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: rat,X1: rat] : or3(bG3(X1,X0),bG4(X1,X0),bG5(X1,X0)),
inference(ennf_transformation,[],[f29]) ).
tff(f29,plain,
! [X0: rat,X1: rat] :
~ ~ or3(bG3(X1,X0),bG4(X1,X0),bG5(X1,X0)),
inference(pure_predicate_removal,[],[f20]) ).
tff(f20,plain,
! [X0: rat,X1: rat] :
~ ( or3(bG3(X1,X0),bG4(X1,X0),bG5(X1,X0))
=> ~ ec3(bG6(X1,X0),bG7(X1,X0),bG8(X1,X0)) ),
inference(fool_elimination,[],[f13,f19,f18,f17,f16,f15,f14]) ).
tff(f15,plain,
! [X1: rat,X0: rat] :
( more(X0,X1)
<=> ( $true = bG4(X1,X0) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG4])]) ).
tff(f17,plain,
! [X1: rat,X0: rat] :
( is(X0,X1)
<=> ( $true = bG6(X1,X0) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG6])]) ).
tff(f18,plain,
! [X1: rat,X0: rat] :
( more(X0,X1)
<=> ( $true = bG7(X1,X0) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG7])]) ).
tff(f19,plain,
! [X1: rat,X0: rat] :
( less(X0,X1)
<=> ( $true = bG8(X1,X0) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG8])]) ).
tff(f13,plain,
! [X0: rat,X1: rat] :
~ ( or3(is(X0,X1),more(X0,X1),less(X0,X1))
=> ~ ec3(is(X0,X1),more(X0,X1),less(X0,X1)) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: rat,X2: rat] :
~ ( or3(is(X1,X2),more(X1,X2),less(X1,X2))
=> ~ ec3(is(X1,X2),more(X1,X2),less(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81) ).
tff(f438,plain,
( ~ spl9_14
| ~ spl9_1
| ~ spl9_5
| spl9_10 ),
inference(avatar_split_clause,[],[f437,f120,f84,f64,f191]) ).
tff(f191,plain,
( spl9_14
<=> or3($true,$true,$true) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
tff(f64,plain,
( spl9_1
<=> ( $true = bG2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
tff(f84,plain,
( spl9_5
<=> ( $true = bG0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
tff(f120,plain,
( spl9_10
<=> or3(bG0,$true,bG2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
tff(f437,plain,
( ~ or3($true,$true,$true)
| ~ spl9_1
| ~ spl9_5
| spl9_10 ),
inference(forward_demodulation,[],[f392,f85]) ).
tff(f85,plain,
( ( $true = bG0 )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f392,plain,
( ~ or3(bG0,$true,$true)
| ~ spl9_1
| spl9_10 ),
inference(forward_demodulation,[],[f122,f65]) ).
tff(f65,plain,
( ( $true = bG2 )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f122,plain,
( ~ or3(bG0,$true,bG2)
| spl9_10 ),
inference(avatar_component_clause,[],[f120]) ).
tff(f425,plain,
( spl9_13
| spl9_4 ),
inference(avatar_split_clause,[],[f423,f78,f187]) ).
tff(f78,plain,
( spl9_4
<=> more(x0,y0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
tff(f423,plain,
( ( $false = bG4(y0,x0) )
| spl9_4 ),
inference(resolution,[],[f79,f160]) ).
tff(f160,plain,
! [X0: rat,X1: rat] :
( more(X1,X0)
| ( $false = bG4(X0,X1) ) ),
inference(trivial_inequality_removal,[],[f159]) ).
tff(f159,plain,
! [X0: rat,X1: rat] :
( ( $true != $true )
| more(X1,X0)
| ( $false = bG4(X0,X1) ) ),
inference(superposition,[],[f50,f6]) ).
tff(f6,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(fool_axiom,[]) ).
tff(f50,plain,
! [X0: rat,X1: rat] :
( ( $true != bG4(X0,X1) )
| more(X1,X0) ),
inference(cnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: rat,X1: rat] :
( ( more(X1,X0)
| ( $true != bG4(X0,X1) ) )
& ( ( $true = bG4(X0,X1) )
| ~ more(X1,X0) ) ),
inference(nnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: rat,X1: rat] :
( more(X1,X0)
<=> ( $true = bG4(X0,X1) ) ),
inference(rectify,[],[f15]) ).
tff(f79,plain,
( ~ more(x0,y0)
| spl9_4 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f422,plain,
( spl9_9
| spl9_3 ),
inference(avatar_split_clause,[],[f421,f74,f116]) ).
tff(f116,plain,
( spl9_9
<=> ( $false = bG1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
tff(f74,plain,
( spl9_3
<=> ( $true = bG1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
tff(f421,plain,
( ( $false = bG1 )
| spl9_3 ),
inference(trivial_inequality_removal,[],[f420]) ).
tff(f420,plain,
( ( $true != $true )
| ( $false = bG1 )
| spl9_3 ),
inference(superposition,[],[f76,f6]) ).
tff(f76,plain,
( ( $true != bG1 )
| spl9_3 ),
inference(avatar_component_clause,[],[f74]) ).
tff(f418,plain,
( ~ spl9_12
| ~ spl9_1 ),
inference(avatar_split_clause,[],[f389,f64,f130]) ).
tff(f130,plain,
( spl9_12
<=> or3(bG0,bG1,$true) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
tff(f389,plain,
( ~ or3(bG0,bG1,$true)
| ~ spl9_1 ),
inference(forward_demodulation,[],[f59,f65]) ).
tff(f59,plain,
~ or3(bG0,bG1,bG2),
inference(cnf_transformation,[],[f27]) ).
tff(f27,plain,
~ or3(bG0,bG1,bG2),
inference(flattening,[],[f10]) ).
tff(f10,plain,
~ or3(bG0,bG1,bG2),
inference(fool_elimination,[],[f4,f9,f8,f7]) ).
tff(f7,plain,
( is(x0,y0)
<=> ( $true = bG0 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG0])]) ).
tff(f8,plain,
( more(x0,y0)
<=> ( $true = bG1 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG1])]) ).
tff(f9,plain,
( less(x0,y0)
<=> ( $true = bG2 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG2])]) ).
tff(f4,negated_conjecture,
~ or3(is(x0,y0),more(x0,y0),less(x0,y0)),
inference(negated_conjecture,[],[f3]) ).
tff(f3,conjecture,
or3(is(x0,y0),more(x0,y0),less(x0,y0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81a) ).
tff(f417,plain,
( ~ spl9_5
| ~ spl9_7 ),
inference(avatar_contradiction_clause,[],[f416]) ).
tff(f416,plain,
( $false
| ~ spl9_5
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f415]) ).
tff(f415,plain,
( ( $true = $false )
| ~ spl9_5
| ~ spl9_7 ),
inference(forward_demodulation,[],[f85,f108]) ).
tff(f108,plain,
( ( $false = bG0 )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f106]) ).
tff(f106,plain,
( spl9_7
<=> ( $false = bG0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
tff(f410,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| ~ spl9_4
| spl9_6
| ~ spl9_7 ),
inference(avatar_contradiction_clause,[],[f409]) ).
tff(f409,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| ~ spl9_4
| spl9_6
| ~ spl9_7 ),
inference(subsumption_resolution,[],[f408,f396]) ).
tff(f396,plain,
( ~ or3($false,$true,$true)
| ~ spl9_1
| ~ spl9_3
| ~ spl9_7 ),
inference(forward_demodulation,[],[f390,f75]) ).
tff(f75,plain,
( ( $true = bG1 )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f74]) ).
tff(f390,plain,
( ~ or3($false,bG1,$true)
| ~ spl9_1
| ~ spl9_7 ),
inference(forward_demodulation,[],[f389,f108]) ).
tff(f408,plain,
( or3($false,$true,$true)
| ~ spl9_2
| ~ spl9_4
| spl9_6 ),
inference(forward_demodulation,[],[f407,f307]) ).
tff(f307,plain,
( ( $false = bG3(y0,x0) )
| spl9_6 ),
inference(resolution,[],[f165,f89]) ).
tff(f89,plain,
( ~ is(x0,y0)
| spl9_6 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f165,plain,
! [X0: rat,X1: rat] :
( is(X1,X0)
| ( $false = bG3(X0,X1) ) ),
inference(trivial_inequality_removal,[],[f164]) ).
tff(f164,plain,
! [X0: rat,X1: rat] :
( ( $true != $true )
| is(X1,X0)
| ( $false = bG3(X0,X1) ) ),
inference(superposition,[],[f52,f6]) ).
tff(f52,plain,
! [X0: rat,X1: rat] :
( ( $true != bG3(X0,X1) )
| is(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
tff(f407,plain,
( or3(bG3(y0,x0),$true,$true)
| ~ spl9_2
| ~ spl9_4 ),
inference(forward_demodulation,[],[f404,f356]) ).
tff(f404,plain,
( or3(bG3(y0,x0),$true,bG5(y0,x0))
| ~ spl9_4 ),
inference(superposition,[],[f61,f394]) ).
tff(f394,plain,
( ( $true = bG4(y0,x0) )
| ~ spl9_4 ),
inference(resolution,[],[f80,f49]) ).
tff(f49,plain,
! [X0: rat,X1: rat] :
( ~ more(X1,X0)
| ( $true = bG4(X0,X1) ) ),
inference(cnf_transformation,[],[f36]) ).
tff(f80,plain,
( more(x0,y0)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f403,plain,
( ~ spl9_14
| ~ spl9_1
| ~ spl9_3
| spl9_8 ),
inference(avatar_split_clause,[],[f402,f110,f74,f64,f191]) ).
tff(f110,plain,
( spl9_8
<=> or3($true,bG1,bG2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
tff(f402,plain,
( ~ or3($true,$true,$true)
| ~ spl9_1
| ~ spl9_3
| spl9_8 ),
inference(forward_demodulation,[],[f391,f75]) ).
tff(f391,plain,
( ~ or3($true,bG1,$true)
| ~ spl9_1
| spl9_8 ),
inference(forward_demodulation,[],[f112,f65]) ).
tff(f112,plain,
( ~ or3($true,bG1,bG2)
| spl9_8 ),
inference(avatar_component_clause,[],[f110]) ).
tff(f388,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f387]) ).
tff(f387,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_13 ),
inference(subsumption_resolution,[],[f386,f363]) ).
tff(f363,plain,
( ~ or3($false,$false,$true)
| ~ spl9_1
| ~ spl9_7
| ~ spl9_9 ),
inference(forward_demodulation,[],[f355,f65]) ).
tff(f355,plain,
( ~ or3($false,$false,bG2)
| ~ spl9_7
| ~ spl9_9 ),
inference(forward_demodulation,[],[f354,f108]) ).
tff(f354,plain,
( ~ or3(bG0,$false,bG2)
| ~ spl9_9 ),
inference(forward_demodulation,[],[f59,f118]) ).
tff(f118,plain,
( ( $false = bG1 )
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f116]) ).
tff(f386,plain,
( or3($false,$false,$true)
| ~ spl9_2
| spl9_6
| ~ spl9_13 ),
inference(forward_demodulation,[],[f385,f307]) ).
tff(f385,plain,
( or3(bG3(y0,x0),$false,$true)
| ~ spl9_2
| ~ spl9_13 ),
inference(forward_demodulation,[],[f382,f356]) ).
tff(f382,plain,
( or3(bG3(y0,x0),$false,bG5(y0,x0))
| ~ spl9_13 ),
inference(superposition,[],[f61,f189]) ).
tff(f347,plain,
( ~ spl9_3
| ~ spl9_9 ),
inference(avatar_contradiction_clause,[],[f346]) ).
tff(f346,plain,
( $false
| ~ spl9_3
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f343]) ).
tff(f343,plain,
( ( $true = $false )
| ~ spl9_3
| ~ spl9_9 ),
inference(backward_demodulation,[],[f75,f118]) ).
tff(f332,plain,
( spl9_2
| ~ spl9_4
| spl9_6
| ~ spl9_7
| spl9_10
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f331]) ).
tff(f331,plain,
( $false
| spl9_2
| ~ spl9_4
| spl9_6
| ~ spl9_7
| spl9_10
| ~ spl9_11 ),
inference(subsumption_resolution,[],[f330,f289]) ).
tff(f289,plain,
( ~ or3($false,$true,$false)
| ~ spl9_7
| spl9_10
| ~ spl9_11 ),
inference(forward_demodulation,[],[f249,f108]) ).
tff(f249,plain,
( ~ or3(bG0,$true,$false)
| spl9_10
| ~ spl9_11 ),
inference(forward_demodulation,[],[f122,f128]) ).
tff(f128,plain,
( ( $false = bG2 )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f126]) ).
tff(f126,plain,
( spl9_11
<=> ( $false = bG2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
tff(f330,plain,
( or3($false,$true,$false)
| spl9_2
| ~ spl9_4
| spl9_6 ),
inference(forward_demodulation,[],[f329,f307]) ).
tff(f329,plain,
( or3(bG3(y0,x0),$true,$false)
| spl9_2
| ~ spl9_4 ),
inference(forward_demodulation,[],[f326,f201]) ).
tff(f201,plain,
( ( $false = bG5(y0,x0) )
| spl9_2 ),
inference(resolution,[],[f69,f156]) ).
tff(f156,plain,
! [X0: rat,X1: rat] :
( less(X1,X0)
| ( $false = bG5(X0,X1) ) ),
inference(trivial_inequality_removal,[],[f155]) ).
tff(f155,plain,
! [X0: rat,X1: rat] :
( ( $true != $true )
| less(X1,X0)
| ( $false = bG5(X0,X1) ) ),
inference(superposition,[],[f48,f6]) ).
tff(f48,plain,
! [X0: rat,X1: rat] :
( ( $true != bG5(X0,X1) )
| less(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
tff(f69,plain,
( ~ less(x0,y0)
| spl9_2 ),
inference(avatar_component_clause,[],[f68]) ).
tff(f326,plain,
( or3(bG3(y0,x0),$true,bG5(y0,x0))
| ~ spl9_4 ),
inference(superposition,[],[f61,f320]) ).
tff(f320,plain,
( ( $true = bG4(y0,x0) )
| ~ spl9_4 ),
inference(resolution,[],[f80,f49]) ).
tff(f315,plain,
( spl9_2
| spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_11
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f314]) ).
tff(f314,plain,
( $false
| spl9_2
| spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_11
| ~ spl9_13 ),
inference(subsumption_resolution,[],[f313,f285]) ).
tff(f285,plain,
( ~ or3($false,$false,$false)
| ~ spl9_7
| ~ spl9_9
| ~ spl9_11 ),
inference(forward_demodulation,[],[f278,f118]) ).
tff(f278,plain,
( ~ or3($false,bG1,$false)
| ~ spl9_7
| ~ spl9_11 ),
inference(backward_demodulation,[],[f245,f108]) ).
tff(f245,plain,
( ~ or3(bG0,bG1,$false)
| ~ spl9_11 ),
inference(forward_demodulation,[],[f59,f128]) ).
tff(f313,plain,
( or3($false,$false,$false)
| spl9_2
| spl9_6
| ~ spl9_13 ),
inference(forward_demodulation,[],[f312,f189]) ).
tff(f312,plain,
( or3($false,bG4(y0,x0),$false)
| spl9_2
| spl9_6 ),
inference(forward_demodulation,[],[f309,f201]) ).
tff(f309,plain,
( or3($false,bG4(y0,x0),bG5(y0,x0))
| spl9_6 ),
inference(superposition,[],[f61,f307]) ).
tff(f264,plain,
( spl9_7
| spl9_5 ),
inference(avatar_split_clause,[],[f263,f84,f106]) ).
tff(f263,plain,
( ( $false = bG0 )
| spl9_5 ),
inference(trivial_inequality_removal,[],[f262]) ).
tff(f262,plain,
( ( $true != $true )
| ( $false = bG0 )
| spl9_5 ),
inference(superposition,[],[f86,f6]) ).
tff(f86,plain,
( ( $true != bG0 )
| spl9_5 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f256,plain,
( ~ spl9_4
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f255]) ).
tff(f255,plain,
( $false
| ~ spl9_4
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f254]) ).
tff(f254,plain,
( ( $true = $false )
| ~ spl9_4
| ~ spl9_13 ),
inference(forward_demodulation,[],[f252,f189]) ).
tff(f252,plain,
( ( $true = bG4(y0,x0) )
| ~ spl9_4 ),
inference(resolution,[],[f80,f49]) ).
tff(f251,plain,
( ~ spl9_16
| ~ spl9_5
| spl9_10
| ~ spl9_11 ),
inference(avatar_split_clause,[],[f250,f126,f120,f84,f230]) ).
tff(f230,plain,
( spl9_16
<=> or3($true,$true,$false) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
tff(f250,plain,
( ~ or3($true,$true,$false)
| ~ spl9_5
| spl9_10
| ~ spl9_11 ),
inference(forward_demodulation,[],[f249,f85]) ).
tff(f244,plain,
( spl9_2
| ~ spl9_5
| ~ spl9_6
| ~ spl9_9
| ~ spl9_11
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f243]) ).
tff(f243,plain,
( $false
| spl9_2
| ~ spl9_5
| ~ spl9_6
| ~ spl9_9
| ~ spl9_11
| ~ spl9_13 ),
inference(subsumption_resolution,[],[f242,f210]) ).
tff(f210,plain,
( ~ or3($true,$false,$false)
| ~ spl9_5
| ~ spl9_9
| ~ spl9_11 ),
inference(backward_demodulation,[],[f197,f128]) ).
tff(f197,plain,
( ~ or3($true,$false,bG2)
| ~ spl9_5
| ~ spl9_9 ),
inference(forward_demodulation,[],[f196,f85]) ).
tff(f196,plain,
( ~ or3(bG0,$false,bG2)
| ~ spl9_9 ),
inference(forward_demodulation,[],[f59,f118]) ).
tff(f242,plain,
( or3($true,$false,$false)
| spl9_2
| ~ spl9_6
| ~ spl9_13 ),
inference(forward_demodulation,[],[f241,f161]) ).
tff(f161,plain,
( ( $true = bG3(y0,x0) )
| ~ spl9_6 ),
inference(resolution,[],[f51,f90]) ).
tff(f241,plain,
( or3(bG3(y0,x0),$false,$false)
| spl9_2
| ~ spl9_13 ),
inference(forward_demodulation,[],[f236,f201]) ).
tff(f236,plain,
( or3(bG3(y0,x0),$false,bG5(y0,x0))
| ~ spl9_13 ),
inference(superposition,[],[f61,f189]) ).
tff(f233,plain,
( spl9_13
| spl9_16
| spl9_2
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f228,f88,f68,f230,f187]) ).
tff(f228,plain,
( or3($true,$true,$false)
| ( $false = bG4(y0,x0) )
| spl9_2
| ~ spl9_6 ),
inference(superposition,[],[f222,f6]) ).
tff(f222,plain,
( or3($true,bG4(y0,x0),$false)
| spl9_2
| ~ spl9_6 ),
inference(forward_demodulation,[],[f219,f161]) ).
tff(f219,plain,
( or3(bG3(y0,x0),bG4(y0,x0),$false)
| spl9_2 ),
inference(superposition,[],[f61,f201]) ).
tff(f215,plain,
( ~ spl9_15
| ~ spl9_5
| ~ spl9_9
| spl9_12 ),
inference(avatar_split_clause,[],[f146,f130,f116,f84,f206]) ).
tff(f146,plain,
( ~ or3($true,$false,$true)
| ~ spl9_5
| ~ spl9_9
| spl9_12 ),
inference(forward_demodulation,[],[f145,f85]) ).
tff(f145,plain,
( ~ or3(bG0,$false,$true)
| ~ spl9_9
| spl9_12 ),
inference(forward_demodulation,[],[f132,f118]) ).
tff(f132,plain,
( ~ or3(bG0,bG1,$true)
| spl9_12 ),
inference(avatar_component_clause,[],[f130]) ).
tff(f200,plain,
( spl9_11
| spl9_1 ),
inference(avatar_split_clause,[],[f199,f64,f126]) ).
tff(f199,plain,
( ( $false = bG2 )
| spl9_1 ),
inference(trivial_inequality_removal,[],[f198]) ).
tff(f198,plain,
( ( $true != $true )
| ( $false = bG2 )
| spl9_1 ),
inference(superposition,[],[f66,f6]) ).
tff(f66,plain,
( ( $true != bG2 )
| spl9_1 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f194,plain,
( spl9_13
| spl9_14
| ~ spl9_2
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f184,f88,f68,f191,f187]) ).
tff(f184,plain,
( or3($true,$true,$true)
| ( $false = bG4(y0,x0) )
| ~ spl9_2
| ~ spl9_6 ),
inference(superposition,[],[f177,f6]) ).
tff(f177,plain,
( or3($true,bG4(y0,x0),$true)
| ~ spl9_2
| ~ spl9_6 ),
inference(forward_demodulation,[],[f172,f154]) ).
tff(f154,plain,
( ( $true = bG5(y0,x0) )
| ~ spl9_2 ),
inference(resolution,[],[f47,f70]) ).
tff(f172,plain,
( or3($true,bG4(y0,x0),bG5(y0,x0))
| ~ spl9_6 ),
inference(superposition,[],[f61,f161]) ).
tff(f123,plain,
( spl9_9
| ~ spl9_10 ),
inference(avatar_split_clause,[],[f97,f120,f116]) ).
tff(f97,plain,
( ~ or3(bG0,$true,bG2)
| ( $false = bG1 ) ),
inference(superposition,[],[f59,f6]) ).
tff(f113,plain,
( spl9_7
| ~ spl9_8 ),
inference(avatar_split_clause,[],[f95,f110,f106]) ).
tff(f95,plain,
( ~ or3($true,bG1,bG2)
| ( $false = bG0 ) ),
inference(superposition,[],[f59,f6]) ).
tff(f92,plain,
( ~ spl9_6
| spl9_5 ),
inference(avatar_split_clause,[],[f57,f84,f88]) ).
tff(f57,plain,
( ( $true = bG0 )
| ~ is(x0,y0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f40,plain,
( ( is(x0,y0)
| ( $true != bG0 ) )
& ( ( $true = bG0 )
| ~ is(x0,y0) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f91,plain,
( ~ spl9_5
| spl9_6 ),
inference(avatar_split_clause,[],[f58,f88,f84]) ).
tff(f58,plain,
( is(x0,y0)
| ( $true != bG0 ) ),
inference(cnf_transformation,[],[f40]) ).
tff(f82,plain,
( ~ spl9_4
| spl9_3 ),
inference(avatar_split_clause,[],[f55,f74,f78]) ).
tff(f55,plain,
( ( $true = bG1 )
| ~ more(x0,y0) ),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
( ( more(x0,y0)
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ more(x0,y0) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f81,plain,
( ~ spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f56,f78,f74]) ).
tff(f56,plain,
( more(x0,y0)
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f39]) ).
tff(f72,plain,
( ~ spl9_2
| spl9_1 ),
inference(avatar_split_clause,[],[f53,f64,f68]) ).
tff(f53,plain,
( ( $true = bG2 )
| ~ less(x0,y0) ),
inference(cnf_transformation,[],[f38]) ).
tff(f38,plain,
( ( less(x0,y0)
| ( $true != bG2 ) )
& ( ( $true = bG2 )
| ~ less(x0,y0) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f71,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f54,f68,f64]) ).
tff(f54,plain,
( less(x0,y0)
| ( $true != bG2 ) ),
inference(cnf_transformation,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM783_8 : TPTP v8.2.0. Released v8.0.0.
% 0.00/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30 % Computer : n012.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon May 20 03:42:23 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % (5734)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32 % (5737)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.15/0.32 % (5739)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.32 % (5738)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.32 % (5740)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.32 % (5735)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.32 % (5741)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.32 % (5736)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.32 Detected minimum model sizes of [1,1,1]
% 0.15/0.32 Detected maximum model sizes of [1,1,2]
% 0.15/0.32 TRYING [1,1,1]
% 0.15/0.32 TRYING [1,1,2]
% 0.15/0.32 Detected minimum model sizes of [1,1]
% 0.15/0.32 Detected maximum model sizes of [2,2]
% 0.15/0.32 Detected minimum model sizes of [1,1]
% 0.15/0.32 Detected maximum model sizes of [2,2]
% 0.15/0.32 TRYING [1,1]
% 0.15/0.32 TRYING [1,1]
% 0.15/0.32 Detected minimum model sizes of [1,1,1]
% 0.15/0.32 Detected maximum model sizes of [1,1,2]
% 0.15/0.32 TRYING [1,1,1]
% 0.15/0.32 TRYING [1,2]
% 0.15/0.32 Cannot enumerate next child to try in an incomplete setup
% 0.15/0.32 TRYING [1,2]
% 0.15/0.32 % (5738)Refutation not found, incomplete strategy% (5738)------------------------------
% 0.15/0.32 % (5738)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.32 % (5738)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32
% 0.15/0.32 % (5738)Memory used [KB]: 740
% 0.15/0.32 % (5738)Time elapsed: 0.004 s
% 0.15/0.32 % (5738)Instructions burned: 5 (million)
% 0.15/0.32 TRYING [1,1,2]
% 0.15/0.32 Cannot enumerate next child to try in an incomplete setup
% 0.15/0.32 % (5738)------------------------------
% 0.15/0.32 % (5738)------------------------------
% 0.15/0.32 % (5735)Refutation not found, incomplete strategy% (5735)------------------------------
% 0.15/0.32 % (5735)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.32 % (5735)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32
% 0.15/0.32 % (5735)Memory used [KB]: 739
% 0.15/0.32 % (5735)Time elapsed: 0.004 s
% 0.15/0.32 % (5735)Instructions burned: 5 (million)
% 0.15/0.32 Cannot enumerate next child to try in an incomplete setup
% 0.15/0.32 % (5741)Refutation not found, incomplete strategy% (5741)------------------------------
% 0.15/0.32 % (5741)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.32 % (5741)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32
% 0.15/0.32 % (5741)Memory used [KB]: 740
% 0.15/0.32 % (5741)Time elapsed: 0.004 s
% 0.15/0.32 % (5741)Instructions burned: 5 (million)
% 0.15/0.32 Cannot enumerate next child to try in an incomplete setup
% 0.15/0.32 % (5736)Refutation not found, incomplete strategy% (5736)------------------------------
% 0.15/0.32 % (5736)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.32 % (5736)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32
% 0.15/0.32 % (5736)Memory used [KB]: 740
% 0.15/0.32 % (5736)Time elapsed: 0.004 s
% 0.15/0.32 % (5736)Instructions burned: 5 (million)
% 0.15/0.32 % (5735)------------------------------
% 0.15/0.32 % (5735)------------------------------
% 0.15/0.32 % (5741)------------------------------
% 0.15/0.32 % (5741)------------------------------
% 0.15/0.32 % (5736)------------------------------
% 0.15/0.32 % (5736)------------------------------
% 0.15/0.33 % (5740)First to succeed.
% 0.15/0.33 % (5740)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5734"
% 0.15/0.33 % (5740)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.33 % (5740)------------------------------
% 0.15/0.33 % (5740)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.33 % (5740)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (5740)Memory used [KB]: 908
% 0.15/0.33 % (5740)Time elapsed: 0.012 s
% 0.15/0.33 % (5740)Instructions burned: 20 (million)
% 0.15/0.33 % (5734)Success in time 0.026 s
%------------------------------------------------------------------------------