TSTP Solution File: NUM666^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 : Sun May 5 08:41:46 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 54 ( 19 unt; 17 typ; 0 def)
% Number of atoms : 337 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 49 ( 22 ~; 18 |; 0 &; 0 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 26 >; 1 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-6 aty)
% Number of variables : 51 ( 9 ^ 36 !; 0 ?; 51 :)
% ( 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,
z: nat ).
thf(func_def_4,type,
some: ( nat > $o ) > $o ).
thf(func_def_5,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_7,type,
moreis: nat > nat > $o ).
thf(func_def_8,type,
lessis: nat > nat > $o ).
thf(func_def_12,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_13,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
vOR: $o > $o > $o ).
thf(func_def_16,type,
vIMP: $o > $o > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f98,plain,
$false,
inference(trivial_inequality_removal,[],[f97]) ).
thf(f97,plain,
$true = $false,
inference(forward_demodulation,[],[f96,f57]) ).
thf(f57,plain,
$false = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f56,plain,
( ( $true != $true )
| ( $false = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)) ) ),
inference(superposition,[],[f23,f8]) ).
thf(f8,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f23,plain,
$true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
$true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
inference(flattening,[],[f10]) ).
thf(f10,plain,
$true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
~ vAPP(sTfun(nat,$o),$o,some,
^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z),X0)),
inference(rectify,[],[f6]) ).
thf(f6,negated_conjecture,
~ vAPP(sTfun(nat,$o),$o,some,
^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z),X0)),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
vAPP(sTfun(nat,$o),$o,some,
^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16d) ).
thf(f96,plain,
$true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f91,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)) ) ),
inference(superposition,[],[f90,f63]) ).
thf(f63,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,z),y),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f60,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,z),y) ) ),
inference(superposition,[],[f24,f26]) ).
thf(f26,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,y),z) = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,y),z) = $true,
inference(fool_elimination,[],[f15]) ).
thf(f15,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,y),z),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,y),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X0) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X0),X1) ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X0) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X0) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).
thf(f90,plain,
! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),y) )
| ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),X0)) ) ),
inference(equality_resolution,[],[f67]) ).
thf(f67,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y) != vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X2),X1) != $true )
| ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X0),X2)) ) ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f64,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X0),X2)) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X2),X1) != $true )
| ( vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y) != vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X0),X1) ) ),
inference(constrained_superposition,[],[f25,f27]) ).
thf(f27,plain,
$true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y)),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
$true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y)),
inference(fool_elimination,[],[f17]) ).
thf(f17,plain,
vAPP(sTfun(nat,$o),$o,some,
^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y),X0)),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(sTfun(nat,$o),$o,some,
^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(f25,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1)) )
| ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0)) )
| ( $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1) ) ),
inference(flattening,[],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0)) )
| ( $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1) ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1) )
=> ( ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1)) )
=> ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0)) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1)
=> ( vAPP(sTfun(nat,$o),$o,some,
^ [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1),X3))
=> vAPP(sTfun(nat,$o),$o,some,
^ [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0),X4)) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X2)
=> ( vAPP(sTfun(nat,$o),$o,some,
^ [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X3),X2),X4))
=> vAPP(sTfun(nat,$o),$o,some,
^ [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X3),X1),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM666^1 : TPTP v8.1.2. 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 : n009.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 : Fri May 3 15:02:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (7705)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (7706)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37 % (7711)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37 % (7709)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37 % (7708)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)
% 0.14/0.37 % (7707)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (7710)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37 % (7712)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)
% 0.14/0.37 % (7709)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.37 % (7708)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.37 % Exception at run slice level% Exception at run slice level
% 0.14/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37 % Exception at run slice level
% 0.14/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37 % Exception at run slice level
% 0.14/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37
% 0.14/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37 % (7711)First to succeed.
% 0.14/0.37 % (7710)Also succeeded, but the first one will report.
% 0.14/0.37 % (7708)Also succeeded, but the first one will report.
% 0.14/0.37 % (7711)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7705"
% 0.14/0.37 % (7711)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (7711)------------------------------
% 0.14/0.38 % (7711)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (7711)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (7711)Memory used [KB]: 778
% 0.14/0.38 % (7711)Time elapsed: 0.007 s
% 0.14/0.38 % (7711)Instructions burned: 9 (million)
% 0.14/0.38 % (7705)Success in time 0.01 s
%------------------------------------------------------------------------------