TSTP Solution File: NUM660^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% 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 02:12:40 EDT 2024
% Result : Theorem 0.13s 0.35s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 59 ( 9 unt; 14 typ; 0 def)
% Number of atoms : 237 ( 51 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 100 ( 46 ~; 35 |; 1 &; 0 @)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 21 >; 1 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 10 con; 0-6 aty)
% Number of variables : 23 ( 0 ^ 17 !; 0 ?; 23 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x: nat ).
thf(func_def_2,type,
y: nat ).
thf(func_def_3,type,
more: nat > nat > $o ).
thf(func_def_5,type,
less: nat > nat > $o ).
thf(func_def_9,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_10,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
vOR: $o > $o > $o ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f87,plain,
$false,
inference(avatar_sat_refutation,[],[f26,f31,f36,f40,f75,f79,f86]) ).
thf(f86,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f85]) ).
thf(f85,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f84,plain,
( ( $true = $false )
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f83,f52]) ).
thf(f52,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $false )
| spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f50,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $false )
| spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f35,f39]) ).
thf(f39,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f38,plain,
( spl0_4
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f35,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true )
| spl0_3 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f33,plain,
( spl0_3
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f83,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $true )
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f80,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $true )
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f78,f74]) ).
thf(f74,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f72,plain,
( spl0_5
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f78,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f77,plain,
( spl0_6
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f79,plain,
spl0_6,
inference(avatar_split_clause,[],[f21,f77]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) = $true )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz11) ).
thf(f75,plain,
( spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f20,f23,f72]) ).
thf(f23,plain,
( spl0_1
<=> ( x = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f20,plain,
( ( x = y )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
( ( x = y )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f14,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
=> ( x = y ) ),
inference(flattening,[],[f10]) ).
thf(f10,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y)
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(f40,plain,
spl0_4,
inference(avatar_split_clause,[],[f6,f38]) ).
thf(f6,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f36,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f18,f33]) ).
thf(f18,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true,
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
( ( x != y )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f13,plain,
~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true )
=> ( x = y ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x)
=> ( x = y ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x)
=> ( x = y ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).
thf(f31,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f5,f28]) ).
thf(f28,plain,
( spl0_2
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f5,plain,
$true != $false,
introduced(fool_axiom,[]) ).
thf(f26,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f19,f23]) ).
thf(f19,plain,
x != y,
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 05:54:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (16305)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35 % (16309)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.35 % Exception at run slice level
% 0.13/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.35 % (16310)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)
% 0.13/0.35 % (16306)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.35 % (16310)First to succeed.
% 0.13/0.35 % Exception at run slice level
% 0.13/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.35 % (16310)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16305"
% 0.13/0.35 % (16310)Refutation found. Thanks to Tanya!
% 0.13/0.35 % SZS status Theorem for theBenchmark
% 0.13/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.35 % (16310)------------------------------
% 0.13/0.35 % (16310)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.35 % (16310)Termination reason: Refutation
% 0.13/0.35
% 0.13/0.35 % (16310)Memory used [KB]: 780
% 0.13/0.35 % (16310)Time elapsed: 0.004 s
% 0.13/0.35 % (16310)Instructions burned: 5 (million)
% 0.13/0.35 % (16305)Success in time 0.01 s
%------------------------------------------------------------------------------