TSTP Solution File: LCL733^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL733^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.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 00:33:56 EDT 2024
% Result : Theorem 0.09s 0.30s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 52 ( 4 unt; 15 typ; 0 def)
% Number of atoms : 332 ( 74 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 127 ( 46 ~; 35 |; 13 &; 0 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 106 ( 105 >; 1 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 6 con; 0-6 aty)
% Number of variables : 112 ( 0 ^ 57 !; 49 ?; 112 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_4,type,
sK0: ( ( b > $o ) > b ) > b > $o ).
thf(func_def_5,type,
sK1: ( ( b > $o ) > b ) > b ).
thf(func_def_6,type,
sK2: ( b > $o ) > b ).
thf(func_def_7,type,
sK3: b > $o ).
thf(func_def_8,type,
sK4: b ).
thf(func_def_10,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_11,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f123,plain,
$false,
inference(avatar_sat_refutation,[],[f55,f113,f117,f122]) ).
thf(f122,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f121]) ).
thf(f121,plain,
( $false
| ~ spl5_1
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f118,plain,
( ( $true != $true )
| ~ spl5_1
| ~ spl5_3 ),
inference(superposition,[],[f116,f51]) ).
thf(f51,plain,
( ( $true = vAPP(b,$o,sK3,sK4) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f49,plain,
( spl5_1
<=> ( $true = vAPP(b,$o,sK3,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
thf(f116,plain,
( ! [X7: b] : ( $true != vAPP(b,$o,sK3,X7) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f115,plain,
( spl5_3
<=> ! [X7: b] : ( $true != vAPP(b,$o,sK3,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
thf(f117,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f17,f53,f115]) ).
thf(f53,plain,
( spl5_2
<=> ! [X4: b > $o,X5: b] :
( ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,sK2,X4)) )
| ( $true != vAPP(b,$o,X4,X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
thf(f17,plain,
! [X7: b,X4: b > $o,X5: b] :
( ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,sK2,X4)) )
| ( $true != vAPP(b,$o,X4,X5) )
| ( $true != vAPP(b,$o,sK3,X7) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
( ! [X0: ( b > $o ) > b] :
( ( $true != vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0),vAPP(sTfun(b,$o),b,X0,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0))) )
& ( $true = vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0),vAPP(sTfun(sTfun(b,$o),b),b,sK1,X0)) ) )
& ( ! [X4: b > $o] :
( ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,sK2,X4)) )
| ! [X5: b] : ( $true != vAPP(b,$o,X4,X5) ) )
| ! [X7: b] :
( ( $true != vAPP(b,$o,sK3,X7) )
& ( $true = vAPP(b,$o,sK3,sK4) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f14,f13,f12,f11,f10]) ).
thf(f10,plain,
! [X0: ( b > $o ) > b] :
( ? [X1: b > $o] :
( ( $true != vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) )
& ? [X2: b] : ( vAPP(b,$o,X1,X2) = $true ) )
=> ( ( $true != vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0),vAPP(sTfun(b,$o),b,X0,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0))) )
& ? [X2: b] : ( $true = vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0),X2) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
! [X0: ( b > $o ) > b] :
( ? [X2: b] : ( $true = vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0),X2) )
=> ( $true = vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0),vAPP(sTfun(sTfun(b,$o),b),b,sK1,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X3: ( b > $o ) > b] :
! [X4: b > $o] :
( ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,X3,X4)) )
| ! [X5: b] : ( $true != vAPP(b,$o,X4,X5) ) )
=> ! [X4: b > $o] :
( ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,sK2,X4)) )
| ! [X5: b] : ( $true != vAPP(b,$o,X4,X5) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X6: b > $o] :
! [X7: b] :
( ( vAPP(b,$o,X6,X7) != $true )
& ? [X8: b] : ( $true = vAPP(b,$o,X6,X8) ) )
=> ! [X7: b] :
( ( $true != vAPP(b,$o,sK3,X7) )
& ? [X8: b] : ( $true = vAPP(b,$o,sK3,X8) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
( ? [X8: b] : ( $true = vAPP(b,$o,sK3,X8) )
=> ( $true = vAPP(b,$o,sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
( ! [X0: ( b > $o ) > b] :
? [X1: b > $o] :
( ( $true != vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) )
& ? [X2: b] : ( vAPP(b,$o,X1,X2) = $true ) )
& ( ? [X3: ( b > $o ) > b] :
! [X4: b > $o] :
( ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,X3,X4)) )
| ! [X5: b] : ( $true != vAPP(b,$o,X4,X5) ) )
| ? [X6: b > $o] :
! [X7: b] :
( ( vAPP(b,$o,X6,X7) != $true )
& ? [X8: b] : ( $true = vAPP(b,$o,X6,X8) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
( ! [X6: ( b > $o ) > b] :
? [X7: b > $o] :
( ( $true != vAPP(b,$o,X7,vAPP(sTfun(b,$o),b,X6,X7)) )
& ? [X8: b] : ( $true = vAPP(b,$o,X7,X8) ) )
& ( ? [X3: ( b > $o ) > b] :
! [X4: b > $o] :
( ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,X3,X4)) )
| ! [X5: b] : ( $true != vAPP(b,$o,X4,X5) ) )
| ? [X0: b > $o] :
! [X1: b] :
( ( $true != vAPP(b,$o,X0,X1) )
& ? [X2: b] : ( $true = vAPP(b,$o,X0,X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ( ( ! [X0: b > $o] :
? [X1: b] :
( ? [X2: b] : ( $true = vAPP(b,$o,X0,X2) )
=> ( $true = vAPP(b,$o,X0,X1) ) )
=> ? [X3: ( b > $o ) > b] :
! [X4: b > $o] :
( ? [X5: b] : ( $true = vAPP(b,$o,X4,X5) )
=> ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,X3,X4)) ) ) )
=> ? [X6: ( b > $o ) > b] :
! [X7: b > $o] :
( ? [X8: b] : ( $true = vAPP(b,$o,X7,X8) )
=> ( $true = vAPP(b,$o,X7,vAPP(sTfun(b,$o),b,X6,X7)) ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,plain,
~ ( ( ! [X1: b > $o] :
? [X2: b] :
( ? [X3: b] : ( vAPP(b,$o,X1,X3) = $true )
=> ( vAPP(b,$o,X1,X2) = $true ) )
=> ? [X4: ( b > $o ) > b] :
! [X5: b > $o] :
( ? [X6: b] : ( $true = vAPP(b,$o,X5,X6) )
=> ( $true = vAPP(b,$o,X5,vAPP(sTfun(b,$o),b,X4,X5)) ) ) )
=> ? [X7: ( b > $o ) > b] :
! [X8: b > $o] :
( ? [X9: b] : ( $true = vAPP(b,$o,X8,X9) )
=> ( $true = vAPP(b,$o,X8,vAPP(sTfun(b,$o),b,X7,X8)) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X1: b > $o] :
? [X2: b] :
( ? [X3: b] : vAPP(b,$o,X1,X3)
=> vAPP(b,$o,X1,X2) )
=> ? [X4: ( b > $o ) > b] :
! [X5: b > $o] :
( ? [X6: b] : vAPP(b,$o,X5,X6)
=> vAPP(b,$o,X5,vAPP(sTfun(b,$o),b,X4,X5)) ) )
=> ? [X7: ( b > $o ) > b] :
! [X8: b > $o] :
( ? [X9: b] : vAPP(b,$o,X8,X9)
=> vAPP(b,$o,X8,vAPP(sTfun(b,$o),b,X7,X8)) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: ( b > $o ) > b > $o] :
( ! [X1: b > $o] :
? [X2: b] :
( ? [X3: b] : vAPP(b,$o,X1,X3)
=> vAPP(b,$o,X1,X2) )
=> ? [X4: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X3: b] : vAPP(b,$o,X1,X3)
=> vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X4,X1)) ) )
=> ? [X5: ( b > $o ) > b] :
! [X6: b > $o] :
( ? [X7: b] : vAPP(b,$o,X6,X7)
=> vAPP(b,$o,X6,vAPP(sTfun(b,$o),b,X5,X6)) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ! [X0: ( b > $o ) > b > $o] :
( ! [X1: b > $o] :
? [X2: b] :
( ? [X3: b] : vAPP(b,$o,X1,X3)
=> vAPP(b,$o,X1,X2) )
=> ? [X4: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X3: b] : vAPP(b,$o,X1,X3)
=> vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X4,X1)) ) )
=> ? [X5: ( b > $o ) > b] :
! [X6: b > $o] :
( ? [X7: b] : vAPP(b,$o,X6,X7)
=> vAPP(b,$o,X6,vAPP(sTfun(b,$o),b,X5,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5310_SUB4) ).
thf(f113,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f112]) ).
thf(f112,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f100,plain,
( ( $true = $false )
| ~ spl5_2 ),
inference(superposition,[],[f91,f18]) ).
thf(f18,plain,
! [X0: ( b > $o ) > b] : ( $true = vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0),vAPP(sTfun(sTfun(b,$o),b),b,sK1,X0)) ),
inference(cnf_transformation,[],[f15]) ).
thf(f91,plain,
( ! [X0: b] : ( $false = vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,sK2),X0) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f82,plain,
( ! [X0: b] :
( ( $true != $true )
| ( $false = vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,sK2),X0) ) )
| ~ spl5_2 ),
inference(superposition,[],[f19,f62]) ).
thf(f62,plain,
( ! [X0: b > $o,X1: b] :
( ( $true = vAPP(b,$o,X0,vAPP(sTfun(b,$o),b,sK2,X0)) )
| ( $false = vAPP(b,$o,X0,X1) ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f61,plain,
( ! [X0: b > $o,X1: b] :
( ( $true != $true )
| ( $true = vAPP(b,$o,X0,vAPP(sTfun(b,$o),b,sK2,X0)) )
| ( $false = vAPP(b,$o,X0,X1) ) )
| ~ spl5_2 ),
inference(superposition,[],[f54,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f54,plain,
( ! [X4: b > $o,X5: b] :
( ( $true != vAPP(b,$o,X4,X5) )
| ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,sK2,X4)) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f19,plain,
! [X0: ( b > $o ) > b] : ( $true != vAPP(b,$o,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0),vAPP(sTfun(b,$o),b,X0,vAPP(sTfun(sTfun(b,$o),b),sTfun(b,$o),sK0,X0))) ),
inference(cnf_transformation,[],[f15]) ).
thf(f55,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f16,f53,f49]) ).
thf(f16,plain,
! [X4: b > $o,X5: b] :
( ( $true = vAPP(b,$o,X4,vAPP(sTfun(b,$o),b,sK2,X4)) )
| ( $true != vAPP(b,$o,X4,X5) )
| ( $true = vAPP(b,$o,sK3,sK4) ) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LCL733^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon May 20 02:19:37 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.09/0.29 % (21831)Running in auto input_syntax mode. Trying TPTP
% 0.09/0.29 % (21832)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.09/0.30 % (21834)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)
% 0.09/0.30 % (21834)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.09/0.30 % (21835)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.09/0.30 % (21836)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.09/0.30 % (21837)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.09/0.30 % (21838)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)
% 0.09/0.30 % (21835)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.09/0.30 % Exception at run slice level
% 0.09/0.30 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.30 % Exception at run slice level
% 0.09/0.30 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.30 % (21834)First to succeed.
% 0.09/0.30 % Exception at run slice level
% 0.09/0.30 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.30 % (21834)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21831"
% 0.09/0.30 % (21834)Refutation found. Thanks to Tanya!
% 0.09/0.30 % SZS status Theorem for theBenchmark
% 0.09/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.30 % (21834)------------------------------
% 0.09/0.30 % (21834)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.09/0.30 % (21834)Termination reason: Refutation
% 0.09/0.30
% 0.09/0.30 % (21834)Memory used [KB]: 858
% 0.09/0.30 % (21834)Time elapsed: 0.005 s
% 0.09/0.30 % (21834)Instructions burned: 9 (million)
% 0.09/0.30 % (21831)Success in time 0.015 s
%------------------------------------------------------------------------------