TSTP Solution File: NUM771^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM771^1 : 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 : n013.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 02:13:22 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 30
% Syntax : Number of formulae : 55 ( 19 unt; 19 typ; 0 def)
% Number of atoms : 387 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 10 avg)
% Number of connectives : 45 ( 22 ~; 17 |; 0 &; 0 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 26 ( 25 >; 1 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 10 con; 0-6 aty)
% Number of variables : 22 ( 0 ^ 16 !; 0 ?; 22 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(func_def_0,type,
frac: $tType ).
thf(func_def_1,type,
x: frac ).
thf(func_def_2,type,
y: frac ).
thf(func_def_3,type,
eq: frac > frac > $o ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
fr: nat > nat > frac ).
thf(func_def_6,type,
ts: nat > nat > nat ).
thf(func_def_7,type,
num: frac > nat ).
thf(func_def_8,type,
den: frac > nat ).
thf(func_def_13,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_14,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_15,type,
vAND: $o > $o > $o ).
thf(func_def_16,type,
vOR: $o > $o > $o ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f77,plain,
$false,
inference(avatar_sat_refutation,[],[f19,f23,f55,f59,f64,f71,f76]) ).
thf(f76,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f75]) ).
thf(f75,plain,
( $false
| ~ spl0_3
| spl0_6 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f72,plain,
( ( $true != $true )
| ~ spl0_3
| spl0_6 ),
inference(superposition,[],[f70,f54]) ).
thf(f54,plain,
( ! [X0: frac] : ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0) = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f53,plain,
( spl0_3
<=> ! [X0: frac] : ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f70,plain,
( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))) )
| spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f68,plain,
( spl0_6
<=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f71,plain,
( ~ spl0_6
| ~ spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f66,f61,f57,f68]) ).
thf(f57,plain,
( spl0_4
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f61,plain,
( spl0_5
<=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,den,x)))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f66,plain,
( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))) )
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f65,f58]) ).
thf(f58,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f65,plain,
( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))) )
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f63,f58]) ).
thf(f63,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,den,x)))) != $true )
| spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f64,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f12,f61]) ).
thf(f12,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,den,x)))) != $true,
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,den,x)))) != $true,
inference(flattening,[],[f8]) ).
thf(f8,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,den,x)))) != $true,
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,den,x)))),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,den,x)))),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,x)),vAPP(frac,nat,num,y))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,x)),vAPP(frac,nat,den,y)))),vAPP(nat,frac,vAPP(nat,sTfun(nat,frac),fr,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,num,y)),vAPP(frac,nat,num,x))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,vAPP(frac,nat,den,y)),vAPP(frac,nat,den,x)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz69) ).
thf(f59,plain,
spl0_4,
inference(avatar_split_clause,[],[f14,f57]) ).
thf(f14,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
thf(f2,axiom,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),ts,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).
thf(f55,plain,
spl0_3,
inference(avatar_split_clause,[],[f13,f53]) ).
thf(f13,plain,
! [X0: frac] : ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0) = $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: frac] : ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0) = $true ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
! [X0: frac] : vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: frac] : vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
thf(f23,plain,
spl0_2,
inference(avatar_split_clause,[],[f6,f21]) ).
thf(f21,plain,
( spl0_2
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f6,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f19,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f5,f16]) ).
thf(f16,plain,
( spl0_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f5,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM771^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n013.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 May 20 06:29:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (25796)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (25801)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)
% 0.14/0.38 % (25801)First to succeed.
% 0.14/0.38 % (25801)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25796"
% 0.14/0.38 % (25798)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (25801)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 % (25801)------------------------------
% 0.14/0.38 % (25801)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (25801)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (25801)Memory used [KB]: 788
% 0.14/0.38 % (25801)Time elapsed: 0.006 s
% 0.14/0.38 % (25801)Instructions burned: 8 (million)
% 0.14/0.38 % (25796)Success in time 0.026 s
%------------------------------------------------------------------------------