TSTP Solution File: SET633^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET633^5 : 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 03:19:49 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 56 ( 3 unt; 14 typ; 0 def)
% Number of atoms : 544 ( 138 equ; 0 cnn)
% Maximal formula atoms : 22 ( 12 avg)
% Number of connectives : 251 ( 87 ~; 79 |; 61 &; 0 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 48 ( 47 >; 1 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 5 con; 0-6 aty)
% Number of variables : 69 ( 0 ^ 45 !; 18 ?; 69 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a ).
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(f88,plain,
$false,
inference(avatar_sat_refutation,[],[f29,f30,f69,f87]) ).
thf(f87,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f86]) ).
thf(f86,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f85,plain,
( ( $true = $false )
| ~ spl4_1
| spl4_2 ),
inference(forward_demodulation,[],[f84,f60]) ).
thf(f60,plain,
$false = vAPP(a,$o,sK2,sK3),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f59,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,sK2,sK3) ) ),
inference(superposition,[],[f20,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f20,plain,
$true != vAPP(a,$o,sK2,sK3),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ( $true != vAPP(a,$o,sK2,sK3) )
& ( ( ( $true != vAPP(a,$o,sK0,sK3) )
& ( $true = vAPP(a,$o,sK1,sK3) ) )
| ( ( $true != vAPP(a,$o,sK1,sK3) )
& ( $true = vAPP(a,$o,sK0,sK3) ) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,sK2,X4) )
| ( $true = vAPP(a,$o,sK0,X4) )
| ( $true != vAPP(a,$o,sK1,X4) ) )
& ! [X5: a] :
( ( $true = vAPP(a,$o,sK2,X5) )
| ( $true = vAPP(a,$o,sK1,X5) )
| ( $true != vAPP(a,$o,sK0,X5) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11]) ).
thf(f11,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( vAPP(a,$o,X2,X3) != $true )
& ( ( ( vAPP(a,$o,X0,X3) != $true )
& ( vAPP(a,$o,X1,X3) = $true ) )
| ( ( vAPP(a,$o,X1,X3) != $true )
& ( vAPP(a,$o,X0,X3) = $true ) ) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X2,X4) )
| ( $true = vAPP(a,$o,X0,X4) )
| ( $true != vAPP(a,$o,X1,X4) ) )
& ! [X5: a] :
( ( $true = vAPP(a,$o,X2,X5) )
| ( $true = vAPP(a,$o,X1,X5) )
| ( $true != vAPP(a,$o,X0,X5) ) ) )
=> ( ? [X3: a] :
( ( $true != vAPP(a,$o,sK2,X3) )
& ( ( ( $true != vAPP(a,$o,sK0,X3) )
& ( $true = vAPP(a,$o,sK1,X3) ) )
| ( ( $true != vAPP(a,$o,sK1,X3) )
& ( $true = vAPP(a,$o,sK0,X3) ) ) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,sK2,X4) )
| ( $true = vAPP(a,$o,sK0,X4) )
| ( $true != vAPP(a,$o,sK1,X4) ) )
& ! [X5: a] :
( ( $true = vAPP(a,$o,sK2,X5) )
| ( $true = vAPP(a,$o,sK1,X5) )
| ( $true != vAPP(a,$o,sK0,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X3: a] :
( ( $true != vAPP(a,$o,sK2,X3) )
& ( ( ( $true != vAPP(a,$o,sK0,X3) )
& ( $true = vAPP(a,$o,sK1,X3) ) )
| ( ( $true != vAPP(a,$o,sK1,X3) )
& ( $true = vAPP(a,$o,sK0,X3) ) ) ) )
=> ( ( $true != vAPP(a,$o,sK2,sK3) )
& ( ( ( $true != vAPP(a,$o,sK0,sK3) )
& ( $true = vAPP(a,$o,sK1,sK3) ) )
| ( ( $true != vAPP(a,$o,sK1,sK3) )
& ( $true = vAPP(a,$o,sK0,sK3) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( vAPP(a,$o,X2,X3) != $true )
& ( ( ( vAPP(a,$o,X0,X3) != $true )
& ( vAPP(a,$o,X1,X3) = $true ) )
| ( ( vAPP(a,$o,X1,X3) != $true )
& ( vAPP(a,$o,X0,X3) = $true ) ) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X2,X4) )
| ( $true = vAPP(a,$o,X0,X4) )
| ( $true != vAPP(a,$o,X1,X4) ) )
& ! [X5: a] :
( ( $true = vAPP(a,$o,X2,X5) )
| ( $true = vAPP(a,$o,X1,X5) )
| ( $true != vAPP(a,$o,X0,X5) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( $true != vAPP(a,$o,X2,X5) )
& ( ( ( $true != vAPP(a,$o,X0,X5) )
& ( $true = vAPP(a,$o,X1,X5) ) )
| ( ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) ) ) )
& ! [X3: a] :
( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X0,X3) = $true )
| ( vAPP(a,$o,X1,X3) != $true ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X2,X4) )
| ( $true = vAPP(a,$o,X1,X4) )
| ( $true != vAPP(a,$o,X0,X4) ) ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( $true != vAPP(a,$o,X2,X5) )
& ( ( ( $true != vAPP(a,$o,X0,X5) )
& ( $true = vAPP(a,$o,X1,X5) ) )
| ( ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) ) ) )
& ! [X3: a] :
( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X0,X3) = $true )
| ( vAPP(a,$o,X1,X3) != $true ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X2,X4) )
| ( $true = vAPP(a,$o,X1,X4) )
| ( $true != vAPP(a,$o,X0,X4) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( vAPP(a,$o,X0,X3) != $true )
& ( vAPP(a,$o,X1,X3) = $true ) )
=> ( vAPP(a,$o,X2,X3) = $true ) )
& ! [X4: a] :
( ( ( $true != vAPP(a,$o,X1,X4) )
& ( $true = vAPP(a,$o,X0,X4) ) )
=> ( $true = vAPP(a,$o,X2,X4) ) ) )
=> ! [X5: a] :
( ( ( ( $true != vAPP(a,$o,X0,X5) )
& ( $true = vAPP(a,$o,X1,X5) ) )
| ( ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) ) )
=> ( $true = vAPP(a,$o,X2,X5) ) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( vAPP(a,$o,X0,X3) != $true )
& ( vAPP(a,$o,X1,X3) = $true ) )
=> ( vAPP(a,$o,X2,X3) = $true ) )
& ! [X4: a] :
( ( ( $true != vAPP(a,$o,X1,X4) )
& ( $true = vAPP(a,$o,X0,X4) ) )
=> ( $true = vAPP(a,$o,X2,X4) ) ) )
=> ! [X5: a] :
( ( ( ( $true != vAPP(a,$o,X0,X5) )
& ( $true = vAPP(a,$o,X1,X5) ) )
| ( ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) ) )
=> ( $true = vAPP(a,$o,X2,X5) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ~ vAPP(a,$o,X0,X3)
& vAPP(a,$o,X1,X3) )
=> vAPP(a,$o,X2,X3) )
& ! [X4: a] :
( ( ~ vAPP(a,$o,X1,X4)
& vAPP(a,$o,X0,X4) )
=> vAPP(a,$o,X2,X4) ) )
=> ! [X5: a] :
( ( ( ~ vAPP(a,$o,X0,X5)
& vAPP(a,$o,X1,X5) )
| ( ~ vAPP(a,$o,X1,X5)
& vAPP(a,$o,X0,X5) ) )
=> vAPP(a,$o,X2,X5) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ~ vAPP(a,$o,X0,X3)
& vAPP(a,$o,X1,X3) )
=> vAPP(a,$o,X2,X3) )
& ! [X3: a] :
( ( ~ vAPP(a,$o,X1,X3)
& vAPP(a,$o,X0,X3) )
=> vAPP(a,$o,X2,X3) ) )
=> ! [X3: a] :
( ( ( ~ vAPP(a,$o,X0,X3)
& vAPP(a,$o,X1,X3) )
| ( ~ vAPP(a,$o,X1,X3)
& vAPP(a,$o,X0,X3) ) )
=> vAPP(a,$o,X2,X3) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ~ vAPP(a,$o,X0,X3)
& vAPP(a,$o,X1,X3) )
=> vAPP(a,$o,X2,X3) )
& ! [X3: a] :
( ( ~ vAPP(a,$o,X1,X3)
& vAPP(a,$o,X0,X3) )
=> vAPP(a,$o,X2,X3) ) )
=> ! [X3: a] :
( ( ( ~ vAPP(a,$o,X0,X3)
& vAPP(a,$o,X1,X3) )
| ( ~ vAPP(a,$o,X1,X3)
& vAPP(a,$o,X0,X3) ) )
=> vAPP(a,$o,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_115_pme) ).
thf(f84,plain,
( ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_1
| spl4_2 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f83,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_1
| spl4_2 ),
inference(forward_demodulation,[],[f82,f71]) ).
thf(f71,plain,
( ( $false = vAPP(a,$o,sK0,sK3) )
| spl4_2 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f70,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,sK0,sK3) )
| spl4_2 ),
inference(superposition,[],[f28,f4]) ).
thf(f28,plain,
( ( $true != vAPP(a,$o,sK0,sK3) )
| spl4_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f26,plain,
( spl4_2
<=> ( $true = vAPP(a,$o,sK0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
thf(f82,plain,
( ( $true = vAPP(a,$o,sK0,sK3) )
| ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f79,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK0,sK3) )
| ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_1 ),
inference(superposition,[],[f15,f23]) ).
thf(f23,plain,
( ( $true = vAPP(a,$o,sK1,sK3) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f22,plain,
( spl4_1
<=> ( $true = vAPP(a,$o,sK1,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
thf(f15,plain,
! [X4: a] :
( ( $true != vAPP(a,$o,sK1,X4) )
| ( $true = vAPP(a,$o,sK0,X4) )
| ( $true = vAPP(a,$o,sK2,X4) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f69,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f68]) ).
thf(f68,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f67,f20]) ).
thf(f67,plain,
( ( $true = vAPP(a,$o,sK2,sK3) )
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f66,f24]) ).
thf(f24,plain,
( ( $true != vAPP(a,$o,sK1,sK3) )
| spl4_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f66,plain,
( ( $true = vAPP(a,$o,sK1,sK3) )
| ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f63,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK1,sK3) )
| ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_2 ),
inference(superposition,[],[f14,f27]) ).
thf(f27,plain,
( ( $true = vAPP(a,$o,sK0,sK3) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f14,plain,
! [X5: a] :
( ( $true != vAPP(a,$o,sK0,X5) )
| ( $true = vAPP(a,$o,sK1,X5) )
| ( $true = vAPP(a,$o,sK2,X5) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f30,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f16,f22,f26]) ).
thf(f16,plain,
( ( $true = vAPP(a,$o,sK1,sK3) )
| ( $true = vAPP(a,$o,sK0,sK3) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f29,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f19,f26,f22]) ).
thf(f19,plain,
( ( $true != vAPP(a,$o,sK0,sK3) )
| ( $true != vAPP(a,$o,sK1,sK3) ) ),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET633^5 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 13:06:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (12424)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (12425)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.39 % (12426)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 % (12428)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.39 % (12429)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.39 % (12430)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.39 % (12427)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)
% 0.15/0.39 % (12431)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)
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% (12428)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39
% 0.15/0.39 % (12427)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % (12430)First to succeed.
% 0.15/0.40 % (12427)Also succeeded, but the first one will report.
% 0.15/0.40 % (12430)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12424"
% 0.15/0.40 % (12429)Also succeeded, but the first one will report.
% 0.15/0.40 % (12430)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (12430)------------------------------
% 0.15/0.40 % (12430)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40 % (12430)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (12430)Memory used [KB]: 772
% 0.15/0.40 % (12430)Time elapsed: 0.010 s
% 0.15/0.40 % (12430)Instructions burned: 7 (million)
% 0.15/0.40 % (12424)Success in time 0.036 s
%------------------------------------------------------------------------------