TSTP Solution File: SYO268^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO268^5 : 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 : n010.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 09:10:47 EDT 2024
% Result : Theorem 0.20s 0.37s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 57 ( 1 unt; 18 typ; 0 def)
% Number of atoms : 374 ( 60 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 134 ( 60 ~; 43 |; 9 &; 0 @)
% ( 8 <=>; 13 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 72 ( 71 >; 1 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 7 con; 0-6 aty)
% Number of variables : 107 ( 0 ^ 62 !; 39 ?; 107 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
r: a > b > $o ).
thf(func_def_6,type,
sK0: ( a > b ) > a ).
thf(func_def_7,type,
sK1: a ).
thf(func_def_8,type,
sK2: a > b ).
thf(func_def_9,type,
sK3: a > b ).
thf(func_def_10,type,
sK4: ( b > $o ) > b ).
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(f93,plain,
$false,
inference(avatar_sat_refutation,[],[f62,f72,f77,f82,f87,f92]) ).
thf(f92,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f91]) ).
thf(f91,plain,
( $false
| ~ spl5_1
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f88]) ).
thf(f88,plain,
( ( $true != $true )
| ~ spl5_1
| ~ spl5_3 ),
inference(superposition,[],[f68,f58]) ).
thf(f58,plain,
( ! [X6: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,sK3,X6)) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f57,plain,
( spl5_1
<=> ! [X6: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,sK3,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
thf(f68,plain,
( ! [X3: b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,sK1),X3) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f67,plain,
( spl5_3
<=> ! [X3: b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,sK1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
thf(f87,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f86]) ).
thf(f86,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f83,plain,
( ( $true != $true )
| ~ spl5_1
| ~ spl5_4 ),
inference(superposition,[],[f71,f58]) ).
thf(f71,plain,
( ! [X0: a > b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,vAPP(sTfun(a,b),a,sK0,X0)),vAPP(a,b,X0,vAPP(sTfun(a,b),a,sK0,X0))) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f70,plain,
( spl5_4
<=> ! [X0: a > b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,vAPP(sTfun(a,b),a,sK0,X0)),vAPP(a,b,X0,vAPP(sTfun(a,b),a,sK0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
thf(f82,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f81]) ).
thf(f81,plain,
( $false
| ~ spl5_2
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f78,plain,
( ( $true != $true )
| ~ spl5_2
| ~ spl5_4 ),
inference(superposition,[],[f71,f61]) ).
thf(f61,plain,
( ! [X5: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X5),vAPP(a,b,sK2,X5)) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f60,plain,
( spl5_2
<=> ! [X5: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X5),vAPP(a,b,sK2,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
thf(f77,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f76]) ).
thf(f76,plain,
( $false
| ~ spl5_2
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f73,plain,
( ( $true != $true )
| ~ spl5_2
| ~ spl5_3 ),
inference(superposition,[],[f68,f61]) ).
thf(f72,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f19,f70,f67]) ).
thf(f19,plain,
! [X3: b,X0: a > b] :
( ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,vAPP(sTfun(a,b),a,sK0,X0)),vAPP(a,b,X0,vAPP(sTfun(a,b),a,sK0,X0))) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,sK1),X3) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
( ( ! [X0: a > b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,vAPP(sTfun(a,b),a,sK0,X0)),vAPP(a,b,X0,vAPP(sTfun(a,b),a,sK0,X0))) )
| ! [X3: b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,sK1),X3) ) )
& ( ! [X5: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X5),vAPP(a,b,sK2,X5)) )
| ! [X6: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,sK3,X6)) ) )
& ! [X9: b > $o] :
( ( $true = vAPP(b,$o,X9,vAPP(sTfun(b,$o),b,sK4,X9)) )
| ! [X10: b] : ( $true != vAPP(b,$o,X9,X10) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f10,f15,f14,f13,f12,f11]) ).
thf(f11,plain,
! [X0: a > b] :
( ? [X1: a] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X1),vAPP(a,b,X0,X1)) )
=> ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,vAPP(sTfun(a,b),a,sK0,X0)),vAPP(a,b,X0,vAPP(sTfun(a,b),a,sK0,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X2: a] :
! [X3: b] : ( vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X2),X3) != $true )
=> ! [X3: b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,sK1),X3) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X4: a > b] :
! [X5: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X5),vAPP(a,b,X4,X5)) )
=> ! [X5: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X5),vAPP(a,b,sK2,X5)) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
! [X6: a] :
( ? [X7: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),X7) )
=> ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,sK3,X6)) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
( ? [X8: ( b > $o ) > b] :
! [X9: b > $o] :
( ( $true = vAPP(b,$o,X9,vAPP(sTfun(b,$o),b,X8,X9)) )
| ! [X10: b] : ( $true != vAPP(b,$o,X9,X10) ) )
=> ! [X9: b > $o] :
( ( $true = vAPP(b,$o,X9,vAPP(sTfun(b,$o),b,sK4,X9)) )
| ! [X10: b] : ( $true != vAPP(b,$o,X9,X10) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ( ! [X0: a > b] :
? [X1: a] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X1),vAPP(a,b,X0,X1)) )
| ? [X2: a] :
! [X3: b] : ( vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X2),X3) != $true ) )
& ( ? [X4: a > b] :
! [X5: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X5),vAPP(a,b,X4,X5)) )
| ! [X6: a] :
? [X7: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),X7) ) )
& ? [X8: ( b > $o ) > b] :
! [X9: b > $o] :
( ( $true = vAPP(b,$o,X9,vAPP(sTfun(b,$o),b,X8,X9)) )
| ! [X10: b] : ( $true != vAPP(b,$o,X9,X10) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,plain,
( ( ! [X5: a > b] :
? [X6: a] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,X5,X6)) )
| ? [X3: a] :
! [X4: b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X3),X4) ) )
& ( ? [X5: a > b] :
! [X6: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,X5,X6)) )
| ! [X3: a] :
? [X4: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X3),X4) ) )
& ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ( vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) = $true )
| ! [X2: b] : ( vAPP(b,$o,X1,X2) != $true ) ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
( ( ! [X5: a > b] :
? [X6: a] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,X5,X6)) )
| ? [X3: a] :
! [X4: b] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X3),X4) ) )
& ( ? [X5: a > b] :
! [X6: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,X5,X6)) )
| ! [X3: a] :
? [X4: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X3),X4) ) )
& ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ( vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) = $true )
| ! [X2: b] : ( vAPP(b,$o,X1,X2) != $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f7,plain,
( ( ! [X3: a] :
? [X4: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X3),X4) )
<~> ? [X5: a > b] :
! [X6: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,X5,X6)) ) )
& ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ( vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) = $true )
| ! [X2: b] : ( vAPP(b,$o,X1,X2) != $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X2: b] : ( vAPP(b,$o,X1,X2) = $true )
=> ( vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) = $true ) )
=> ( ! [X3: a] :
? [X4: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X3),X4) )
<=> ? [X5: a > b] :
! [X6: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,X5,X6)) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X2: b] : vAPP(b,$o,X1,X2)
=> vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) )
=> ( ! [X3: a] :
? [X4: b] : vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X3),X4)
<=> ? [X5: a > b] :
! [X6: a] : vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,X5,X6)) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X2: b] : vAPP(b,$o,X1,X2)
=> vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) )
=> ( ! [X2: a] :
? [X3: b] : vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X2),X3)
<=> ? [X4: a > b] :
! [X2: a] : vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X2),vAPP(a,b,X4,X2)) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X2: b] : vAPP(b,$o,X1,X2)
=> vAPP(b,$o,X1,vAPP(sTfun(b,$o),b,X0,X1)) )
=> ( ! [X2: a] :
? [X3: b] : vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X2),X3)
<=> ? [X4: a > b] :
! [X2: a] : vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X2),vAPP(a,b,X4,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5308) ).
thf(f62,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f18,f60,f57]) ).
thf(f18,plain,
! [X6: a,X5: a] :
( ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X5),vAPP(a,b,sK2,X5)) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),r,X6),vAPP(a,b,sK3,X6)) ) ),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO268^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n010.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 10:14:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (9626)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (9633)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)
% 0.13/0.36 % Exception at run slice level
% 0.13/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.36 % (9628)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36 % (9629)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)
% 0.13/0.36 % (9630)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.36 % (9627)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.36 % (9631)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.20/0.36 % (9632)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.20/0.36 % (9629)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.36 % (9630)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.36 % Exception at run slice level
% 0.20/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.37 % Exception at run slice level
% 0.20/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.37 % Exception at run slice level
% 0.20/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.37 % (9629)First to succeed.
% 0.20/0.37 % (9632)Also succeeded, but the first one will report.
% 0.20/0.37 % (9629)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9626"
% 0.20/0.37 % (9629)Refutation found. Thanks to Tanya!
% 0.20/0.37 % SZS status Theorem for theBenchmark
% 0.20/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.37 % (9629)------------------------------
% 0.20/0.37 % (9629)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.37 % (9629)Termination reason: Refutation
% 0.20/0.37
% 0.20/0.37 % (9629)Memory used [KB]: 849
% 0.20/0.37 % (9629)Time elapsed: 0.006 s
% 0.20/0.37 % (9629)Instructions burned: 8 (million)
% 0.20/0.37 % (9626)Success in time 0.019 s
%------------------------------------------------------------------------------