TSTP Solution File: SET014^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET014^5 : 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 : n027.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 03:14:21 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 47 ( 5 unt; 14 typ; 0 def)
% Number of atoms : 312 ( 79 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 127 ( 41 ~; 42 |; 24 &; 0 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 45 ( 44 >; 1 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 5 con; 0-6 aty)
% Number of variables : 63 ( 0 ^ 39 !; 18 ?; 63 :)
% ( 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(f73,plain,
$false,
inference(avatar_sat_refutation,[],[f62,f67,f72]) ).
thf(f72,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f71]) ).
thf(f71,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f70,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f69,f28]) ).
thf(f28,plain,
$false = vAPP(a,$o,sK2,sK3),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f26,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,sK2,sK3) ) ),
inference(superposition,[],[f16,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f16,plain,
$true != vAPP(a,$o,sK2,sK3),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
( ( $true != vAPP(a,$o,sK2,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,sK1,X4) ) )
& ! [X5: a] :
( ( $true = vAPP(a,$o,sK2,X5) )
| ( $true != vAPP(a,$o,sK0,X5) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( vAPP(a,$o,X2,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,X1,X4) ) )
& ! [X5: a] :
( ( $true = vAPP(a,$o,X2,X5) )
| ( $true != vAPP(a,$o,X0,X5) ) ) )
=> ( ? [X3: a] :
( ( $true != vAPP(a,$o,sK2,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,sK1,X4) ) )
& ! [X5: a] :
( ( $true = vAPP(a,$o,sK2,X5) )
| ( $true != vAPP(a,$o,sK0,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
( ? [X3: a] :
( ( $true != vAPP(a,$o,sK2,X3) )
& ( ( $true = vAPP(a,$o,sK1,X3) )
| ( $true = vAPP(a,$o,sK0,X3) ) ) )
=> ( ( $true != vAPP(a,$o,sK2,sK3) )
& ( ( $true = vAPP(a,$o,sK1,sK3) )
| ( $true = vAPP(a,$o,sK0,sK3) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( vAPP(a,$o,X2,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,X1,X4) ) )
& ! [X5: a] :
( ( $true = vAPP(a,$o,X2,X5) )
| ( $true != vAPP(a,$o,X0,X5) ) ) ),
inference(rectify,[],[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,X1,X5) )
| ( $true = vAPP(a,$o,X0,X5) ) ) )
& ! [X3: a] :
( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X1,X3) != $true ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X2,X4) )
| ( $true != vAPP(a,$o,X0,X4) ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( $true != vAPP(a,$o,X2,X5) )
& ( ( $true = vAPP(a,$o,X1,X5) )
| ( $true = vAPP(a,$o,X0,X5) ) ) )
& ! [X3: a] :
( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X1,X3) != $true ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X2,X4) )
| ( $true != vAPP(a,$o,X0,X4) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( vAPP(a,$o,X1,X3) = $true )
=> ( vAPP(a,$o,X2,X3) = $true ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X0,X4) )
=> ( $true = vAPP(a,$o,X2,X4) ) ) )
=> ! [X5: a] :
( ( ( $true = vAPP(a,$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,X1,X3)
=> vAPP(a,$o,X2,X3) )
& ! [X4: a] :
( vAPP(a,$o,X0,X4)
=> vAPP(a,$o,X2,X4) ) )
=> ! [X5: a] :
( ( vAPP(a,$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,X1,X3)
=> vAPP(a,$o,X2,X3) )
& ! [X3: a] :
( vAPP(a,$o,X0,X3)
=> vAPP(a,$o,X2,X3) ) )
=> ! [X3: a] :
( ( vAPP(a,$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,X1,X3)
=> vAPP(a,$o,X2,X3) )
& ! [X3: a] :
( vAPP(a,$o,X0,X3)
=> vAPP(a,$o,X2,X3) ) )
=> ! [X3: a] :
( ( vAPP(a,$o,X1,X3)
| vAPP(a,$o,X0,X3) )
=> vAPP(a,$o,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_32_pme) ).
thf(f69,plain,
( ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f68,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_1 ),
inference(superposition,[],[f13,f57]) ).
thf(f57,plain,
( ( $true = vAPP(a,$o,sK0,sK3) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f55,plain,
( spl4_1
<=> ( $true = vAPP(a,$o,sK0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
thf(f13,plain,
! [X5: a] :
( ( $true != vAPP(a,$o,sK0,X5) )
| ( $true = vAPP(a,$o,sK2,X5) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f67,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f66]) ).
thf(f66,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f65,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f64,f28]) ).
thf(f64,plain,
( ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f63,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK2,sK3) )
| ~ spl4_2 ),
inference(superposition,[],[f14,f61]) ).
thf(f61,plain,
( ( $true = vAPP(a,$o,sK1,sK3) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f59,plain,
( spl4_2
<=> ( $true = vAPP(a,$o,sK1,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
thf(f14,plain,
! [X4: a] :
( ( $true != vAPP(a,$o,sK1,X4) )
| ( $true = vAPP(a,$o,sK2,X4) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f62,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f15,f59,f55]) ).
thf(f15,plain,
( ( $true = vAPP(a,$o,sK1,sK3) )
| ( $true = vAPP(a,$o,sK0,sK3) ) ),
inference(cnf_transformation,[],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET014^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n027.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 11:36:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (18119)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (18122)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 % (18126)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 % (18122)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 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 % (18122)First to succeed.
% 0.13/0.37 % (18122)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18119"
% 0.13/0.37 % (18125)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37 % (18122)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37 % (18122)------------------------------
% 0.13/0.37 % (18122)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37 % (18122)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (18122)Memory used [KB]: 771
% 0.13/0.37 % (18122)Time elapsed: 0.005 s
% 0.13/0.37 % (18122)Instructions burned: 5 (million)
% 0.13/0.37 % (18119)Success in time 0.019 s
%------------------------------------------------------------------------------