TSTP Solution File: NUM667^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM667^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 02:12:43 EDT 2024
% Result : Theorem 0.17s 0.34s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 66 ( 4 unt; 14 typ; 0 def)
% Number of atoms : 316 ( 73 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 132 ( 62 ~; 38 |; 3 &; 0 @)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 19 >; 1 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-6 aty)
% Number of variables : 29 ( 0 ^ 23 !; 0 ?; 29 :)
% ( 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,
less: nat > nat > $o ).
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(f130,plain,
$false,
inference(avatar_sat_refutation,[],[f89,f100,f109,f114,f129]) ).
thf(f129,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f128]) ).
thf(f128,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f127,f36]) ).
thf(f36,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) != $true,
inference(cnf_transformation,[],[f28]) ).
thf(f28,plain,
( ( x != z )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) != $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f22,plain,
~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) != $true )
=> ( x = z ) ),
inference(flattening,[],[f11]) ).
thf(f11,plain,
~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) != $true )
=> ( x = z ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z)
=> ( x = z ) ),
inference(rectify,[],[f7]) ).
thf(f7,negated_conjecture,
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z)
=> ( x = z ) ),
inference(negated_conjecture,[],[f6]) ).
thf(f6,conjecture,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z)
=> ( x = z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz17) ).
thf(f127,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f124,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f121,f104]) ).
thf(f104,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f102,plain,
( spl0_3
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f121,plain,
( ! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),X0) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f116,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),X0) ) )
| ~ spl0_1 ),
inference(superposition,[],[f41,f84]) ).
thf(f84,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f82,plain,
( spl0_1
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f41,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f33,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) != $true )
| ( ( X0 != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ) ),
inference(flattening,[],[f32]) ).
thf(f32,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) != $true )
| ( ( X0 != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f26,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
=> ( X0 = X1 ) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) ) ) ),
inference(flattening,[],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
=> ( X0 = X1 ) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1)
=> ( X0 = X1 ) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2)
=> ( X1 = X2 ) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X2),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
thf(f114,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f113]) ).
thf(f113,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f111,f84]) ).
thf(f111,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true )
| ~ spl0_4 ),
inference(superposition,[],[f36,f108]) ).
thf(f108,plain,
( ( y = z )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f106,plain,
( spl0_4
<=> ( y = z ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f109,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f39,f106,f102]) ).
thf(f39,plain,
( ( y = z )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f30,plain,
( ( y = z )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f24,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) != $true )
=> ( y = z ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) != $true )
=> ( y = z ) ),
inference(fool_elimination,[],[f14]) ).
thf(f14,plain,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z)
=> ( y = z ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z)
=> ( y = z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(f100,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f99]) ).
thf(f99,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f98,f36]) ).
thf(f98,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f97,f88]) ).
thf(f88,plain,
( ( x = y )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f86,plain,
( spl0_2
<=> ( x = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f97,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true )
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f96,f37]) ).
thf(f37,plain,
x != z,
inference(cnf_transformation,[],[f28]) ).
thf(f96,plain,
( ( x = z )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f39,f88]) ).
thf(f89,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f38,f86,f82]) ).
thf(f38,plain,
( ( x = y )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f29,plain,
( ( x = y )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f23,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true )
=> ( x = y ) ),
inference(flattening,[],[f13]) ).
thf(f13,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y)
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM667^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 06:59:38 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (19409)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.33 % (19412)WARNING: value z3 for option sas not known
% 0.17/0.34 % (19412)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.34 % (19411)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.34 % (19413)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.34 % (19410)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.34 % Exception at run slice level% (19414)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.34
% 0.17/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34 % Exception at run slice level
% 0.17/0.34 User error: % (19415)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.34 Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34 % Exception at run slice level
% 0.17/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34 % (19416)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.34 % (19416)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.34 % (19412)First to succeed.
% 0.17/0.34 % (19415)Also succeeded, but the first one will report.
% 0.17/0.34 % (19414)Also succeeded, but the first one will report.
% 0.17/0.34 % (19412)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19409"
% 0.17/0.34 % (19416)Also succeeded, but the first one will report.
% 0.17/0.34 % (19412)Refutation found. Thanks to Tanya!
% 0.17/0.34 % SZS status Theorem for theBenchmark
% 0.17/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.34 % (19412)------------------------------
% 0.17/0.34 % (19412)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.34 % (19412)Termination reason: Refutation
% 0.17/0.34
% 0.17/0.34 % (19412)Memory used [KB]: 782
% 0.17/0.34 % (19412)Time elapsed: 0.006 s
% 0.17/0.34 % (19412)Instructions burned: 8 (million)
% 0.17/0.34 % (19409)Success in time 0.017 s
%------------------------------------------------------------------------------