TSTP Solution File: DAT031_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT031_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 Apr 30 11:03:43 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 55
% Syntax : Number of formulae : 134 ( 38 unt; 6 typ; 0 def)
% Number of atoms : 317 ( 49 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 316 ( 127 ~; 131 |; 20 &)
% ( 34 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 373 ( 67 atm; 72 fun; 91 num; 143 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 35 ( 31 usr; 31 prp; 0-2 aty)
% Number of functors : 13 ( 4 usr; 9 con; 0-2 aty)
% Number of variables : 175 ( 170 !; 5 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_12,type,
sK0: collection ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f273,plain,
$false,
inference(avatar_sat_refutation,[],[f49,f53,f57,f61,f65,f69,f73,f77,f82,f86,f90,f94,f98,f102,f110,f118,f122,f134,f138,f164,f168,f172,f199,f205,f210,f216,f225,f229,f233,f269,f272]) ).
tff(f272,plain,
( ~ spl1_2
| ~ spl1_25 ),
inference(avatar_contradiction_clause,[],[f271]) ).
tff(f271,plain,
( $false
| ~ spl1_2
| ~ spl1_25 ),
inference(evaluation,[],[f270]) ).
tff(f270,plain,
( $less(40,30)
| $less(30,20)
| ~ spl1_2
| ~ spl1_25 ),
inference(resolution,[],[f209,f52]) ).
tff(f52,plain,
( ! [X1: $int] :
( ~ in(X1,sK0)
| $less(40,X1)
| $less(X1,20) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f51]) ).
tff(f51,plain,
( spl1_2
<=> ! [X1: $int] :
( ~ in(X1,sK0)
| $less(40,X1)
| $less(X1,20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f209,plain,
( in(30,sK0)
| ~ spl1_25 ),
inference(avatar_component_clause,[],[f207]) ).
tff(f207,plain,
( spl1_25
<=> in(30,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
tff(f269,plain,
( spl1_30
| ~ spl1_9
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f153,f136,f80,f267]) ).
tff(f267,plain,
( spl1_30
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
tff(f80,plain,
( spl1_9
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
tff(f136,plain,
( spl1_19
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
tff(f153,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl1_9
| ~ spl1_19 ),
inference(superposition,[],[f137,f81]) ).
tff(f81,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f80]) ).
tff(f137,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f136]) ).
tff(f233,plain,
( spl1_29
| ~ spl1_9
| ~ spl1_20 ),
inference(avatar_split_clause,[],[f188,f162,f80,f231]) ).
tff(f231,plain,
( spl1_29
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
tff(f162,plain,
( spl1_20
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
tff(f188,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl1_9
| ~ spl1_20 ),
inference(evaluation,[],[f173]) ).
tff(f173,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl1_9
| ~ spl1_20 ),
inference(superposition,[],[f163,f81]) ).
tff(f163,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f162]) ).
tff(f229,plain,
( spl1_28
| ~ spl1_10
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f112,f92,f84,f227]) ).
tff(f227,plain,
( spl1_28
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
tff(f84,plain,
( spl1_10
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
tff(f92,plain,
( spl1_12
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
tff(f112,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl1_10
| ~ spl1_12 ),
inference(superposition,[],[f93,f85]) ).
tff(f85,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f93,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f92]) ).
tff(f225,plain,
( spl1_27
| ~ spl1_10
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f104,f88,f84,f223]) ).
tff(f223,plain,
( spl1_27
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
tff(f88,plain,
( spl1_11
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
tff(f104,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl1_10
| ~ spl1_11 ),
inference(superposition,[],[f89,f85]) ).
tff(f89,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f216,plain,
( spl1_26
| ~ spl1_3
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f103,f88,f55,f214]) ).
tff(f214,plain,
( spl1_26
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
tff(f55,plain,
( spl1_3
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f103,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl1_3
| ~ spl1_11 ),
inference(resolution,[],[f89,f56]) ).
tff(f56,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f55]) ).
tff(f210,plain,
( spl1_25
| ~ spl1_8
| ~ spl1_23 ),
inference(avatar_split_clause,[],[f200,f197,f75,f207]) ).
tff(f75,plain,
( spl1_8
<=> ! [X0: $int,X1: collection] : in(X0,add(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
tff(f197,plain,
( spl1_23
<=> ! [X0: $int] :
( in(X0,sK0)
| ~ in(X0,add(30,add(50,empty))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
tff(f200,plain,
( in(30,sK0)
| ~ spl1_8
| ~ spl1_23 ),
inference(resolution,[],[f198,f76]) ).
tff(f76,plain,
( ! [X0: $int,X1: collection] : in(X0,add(X0,X1))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f75]) ).
tff(f198,plain,
( ! [X0: $int] :
( ~ in(X0,add(30,add(50,empty)))
| in(X0,sK0) )
| ~ spl1_23 ),
inference(avatar_component_clause,[],[f197]) ).
tff(f205,plain,
( spl1_24
| ~ spl1_1
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f195,f170,f46,f203]) ).
tff(f203,plain,
( spl1_24
<=> ! [X0: $int] :
( ~ in(X0,sK0)
| in(X0,add(30,add(50,empty)))
| ( 10 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
tff(f46,plain,
( spl1_1
<=> ( add(10,add(30,add(50,empty))) = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f170,plain,
( spl1_22
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
tff(f195,plain,
( ! [X0: $int] :
( ~ in(X0,sK0)
| in(X0,add(30,add(50,empty)))
| ( 10 = X0 ) )
| ~ spl1_1
| ~ spl1_22 ),
inference(superposition,[],[f171,f48]) ).
tff(f48,plain,
( ( add(10,add(30,add(50,empty))) = sK0 )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f46]) ).
tff(f171,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,add(X2,X1))
| in(X0,X1)
| ( X0 = X2 ) )
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f170]) ).
tff(f199,plain,
( spl1_23
| ~ spl1_1
| ~ spl1_14 ),
inference(avatar_split_clause,[],[f114,f100,f46,f197]) ).
tff(f100,plain,
( spl1_14
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
tff(f114,plain,
( ! [X0: $int] :
( in(X0,sK0)
| ~ in(X0,add(30,add(50,empty))) )
| ~ spl1_1
| ~ spl1_14 ),
inference(superposition,[],[f101,f48]) ).
tff(f101,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) )
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f172,plain,
spl1_22,
inference(avatar_split_clause,[],[f42,f170]) ).
tff(f42,plain,
! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(flattening,[],[f30]) ).
tff(f30,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1) )
<=> in(X0,add(X2,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X5: $int,X6: collection,X7: $int] :
( ( ( X5 = X7 )
| in(X5,X6) )
<=> in(X5,add(X7,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f168,plain,
spl1_21,
inference(avatar_split_clause,[],[f37,f166]) ).
tff(f166,plain,
( spl1_21
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
tff(f37,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tff(f29,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f28]) ).
tff(f28,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 != X2 )
& in(X0,X1) )
<=> in(X0,remove(X2,X1)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: $int,X9: collection,X10: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(f164,plain,
spl1_20,
inference(avatar_split_clause,[],[f10,f162]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f138,plain,
spl1_19,
inference(avatar_split_clause,[],[f17,f136]) ).
tff(f17,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f134,plain,
spl1_18,
inference(avatar_split_clause,[],[f12,f132]) ).
tff(f132,plain,
( spl1_18
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
tff(f12,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f122,plain,
spl1_17,
inference(avatar_split_clause,[],[f16,f120]) ).
tff(f120,plain,
( spl1_17
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
tff(f16,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f118,plain,
spl1_16,
inference(avatar_split_clause,[],[f15,f116]) ).
tff(f116,plain,
( spl1_16
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
tff(f15,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f110,plain,
( spl1_15
| ~ spl1_1
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f78,f75,f46,f107]) ).
tff(f107,plain,
( spl1_15
<=> in(10,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
tff(f78,plain,
( in(10,sK0)
| ~ spl1_1
| ~ spl1_8 ),
inference(superposition,[],[f76,f48]) ).
tff(f102,plain,
spl1_14,
inference(avatar_split_clause,[],[f40,f100]) ).
tff(f40,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tff(f98,plain,
spl1_13,
inference(avatar_split_clause,[],[f38,f96]) ).
tff(f96,plain,
( spl1_13
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
tff(f38,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ),
inference(cnf_transformation,[],[f29]) ).
tff(f94,plain,
spl1_12,
inference(avatar_split_clause,[],[f20,f92]) ).
tff(f20,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f90,plain,
spl1_11,
inference(avatar_split_clause,[],[f18,f88]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f86,plain,
spl1_10,
inference(avatar_split_clause,[],[f9,f84]) ).
tff(f9,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f82,plain,
spl1_9,
inference(avatar_split_clause,[],[f13,f80]) ).
tff(f13,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f77,plain,
spl1_8,
inference(avatar_split_clause,[],[f36,f75]) ).
tff(f36,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(cnf_transformation,[],[f22]) ).
tff(f22,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f73,plain,
spl1_7,
inference(avatar_split_clause,[],[f35,f71]) ).
tff(f71,plain,
( spl1_7
<=> ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
tff(f35,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(cnf_transformation,[],[f21]) ).
tff(f21,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X3: $int,X4: collection] : ~ in(X3,remove(X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f69,plain,
spl1_6,
inference(avatar_split_clause,[],[f19,f67]) ).
tff(f67,plain,
( spl1_6
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f19,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f65,plain,
spl1_5,
inference(avatar_split_clause,[],[f11,f63]) ).
tff(f63,plain,
( spl1_5
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f11,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f61,plain,
spl1_4,
inference(avatar_split_clause,[],[f34,f59]) ).
tff(f59,plain,
( spl1_4
<=> ! [X0: $int] : ~ in(X0,empty) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f34,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(f57,plain,
spl1_3,
inference(avatar_split_clause,[],[f14,f55]) ).
tff(f14,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f53,plain,
spl1_2,
inference(avatar_split_clause,[],[f33,f51]) ).
tff(f33,plain,
! [X1: $int] :
( ~ in(X1,sK0)
| $less(40,X1)
| $less(X1,20) ),
inference(cnf_transformation,[],[f27]) ).
tff(f27,plain,
( ! [X1: $int] :
( ~ in(X1,sK0)
| $less(40,X1)
| $less(X1,20) )
& ( add(10,add(30,add(50,empty))) = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f25,f26]) ).
tff(f26,plain,
( ? [X0: collection] :
( ! [X1: $int] :
( ~ in(X1,X0)
| $less(40,X1)
| $less(X1,20) )
& ( add(10,add(30,add(50,empty))) = X0 ) )
=> ( ! [X1: $int] :
( ~ in(X1,sK0)
| $less(40,X1)
| $less(X1,20) )
& ( add(10,add(30,add(50,empty))) = sK0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f25,plain,
? [X0: collection] :
( ! [X1: $int] :
( ~ in(X1,X0)
| $less(40,X1)
| $less(X1,20) )
& ( add(10,add(30,add(50,empty))) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,plain,
~ ! [X0: collection] :
( ( add(10,add(30,add(50,empty))) = X0 )
=> ? [X1: $int] :
( in(X1,X0)
& ~ $less(40,X1)
& ~ $less(X1,20) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ! [X0: collection] :
( ( add(10,add(30,add(50,empty))) = X0 )
=> ? [X1: $int] :
( in(X1,X0)
& $lesseq(X1,40)
& $lesseq(20,X1) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
! [X0: collection] :
( ( add(10,add(30,add(50,empty))) = X0 )
=> ? [X1: $int] :
( in(X1,X0)
& $lesseq(X1,40)
& $lesseq(20,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f49,plain,
spl1_1,
inference(avatar_split_clause,[],[f32,f46]) ).
tff(f32,plain,
add(10,add(30,add(50,empty))) = sK0,
inference(cnf_transformation,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : DAT031_1 : TPTP v8.1.2. Released v5.0.0.
% 0.09/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n005.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 : Mon Apr 29 22:07:41 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (6276)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (6281)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (6279)WARNING: value z3 for option sas not known
% 0.14/0.37 % (6278)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (6280)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (6279)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (6277)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (6282)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (6283)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 % (6278)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (6278)Terminated due to inappropriate strategy.
% 0.14/0.37 % (6278)------------------------------
% 0.14/0.37 % (6278)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.37 % (6278)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (6278)Memory used [KB]: 745
% 0.14/0.37 % (6278)Time elapsed: 0.002 s
% 0.14/0.37 % (6278)Instructions burned: 2 (million)
% 0.14/0.37 % (6278)------------------------------
% 0.14/0.37 % (6278)------------------------------
% 0.14/0.37 % (6280)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (6280)Terminated due to inappropriate strategy.
% 0.14/0.37 % (6280)------------------------------
% 0.14/0.37 % (6280)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.37 % (6280)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (6277)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (6280)Memory used [KB]: 745
% 0.14/0.37 % (6280)Time elapsed: 0.002 s
% 0.14/0.37 % (6280)Instructions burned: 2 (million)
% 0.14/0.37 % (6280)------------------------------
% 0.14/0.37 % (6280)------------------------------
% 0.14/0.37 % (6277)Terminated due to inappropriate strategy.
% 0.14/0.37 % (6277)------------------------------
% 0.14/0.37 % (6277)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.37 % (6277)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (6277)Memory used [KB]: 745
% 0.14/0.37 % (6277)Time elapsed: 0.002 s
% 0.14/0.37 % (6277)Instructions burned: 2 (million)
% 0.14/0.37 % (6277)------------------------------
% 0.14/0.37 % (6277)------------------------------
% 0.14/0.37 % (6281)First to succeed.
% 0.14/0.37 % (6279)Also succeeded, but the first one will report.
% 0.14/0.38 % (6281)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (6281)------------------------------
% 0.14/0.38 % (6281)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (6281)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (6281)Memory used [KB]: 919
% 0.14/0.38 % (6281)Time elapsed: 0.009 s
% 0.14/0.38 % (6281)Instructions burned: 13 (million)
% 0.14/0.38 % (6281)------------------------------
% 0.14/0.38 % (6281)------------------------------
% 0.14/0.38 % (6276)Success in time 0.02 s
%------------------------------------------------------------------------------