TSTP Solution File: NUM682^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 : Sun May 5 08:41:50 EDT 2024
% Result : Theorem 0.12s 0.37s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 56 ( 15 unt; 16 typ; 0 def)
% Number of atoms : 394 ( 76 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 125 ( 67 ~; 23 |; 4 &; 0 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 23 >; 1 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 5 con; 0-6 aty)
% Number of variables : 58 ( 0 ^ 52 !; 0 ?; 58 :)
% ( 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_5,type,
pl: nat > nat > nat ).
thf(func_def_7,type,
more: nat > nat > $o ).
thf(func_def_11,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_12,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
vOR: $o > $o > $o ).
thf(func_def_15,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f132,plain,
$false,
inference(subsumption_resolution,[],[f129,f45]) ).
thf(f45,plain,
! [X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X1) ),
inference(equality_resolution,[],[f40]) ).
thf(f40,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f32,plain,
! [X0: nat,X1: nat] :
( ( ( X0 != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) )
& ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) )
& ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
| ( X0 != X1 ) ) ),
inference(flattening,[],[f31]) ).
thf(f31,plain,
! [X0: nat,X1: nat] :
( ( ( X0 != X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) )
& ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) )
& ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f26,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
=> ( X0 != X1 ) ) ) ),
inference(flattening,[],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) )
=> ~ ~ ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
=> ( X0 != X1 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ~ ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
=> ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1)
=> ( X0 != X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X1: nat,X2: nat] :
~ ( ( ( X1 = X2 )
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2) )
=> ~ ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) )
=> ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2)
=> ( X1 != X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10b) ).
thf(f129,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),
inference(superposition,[],[f43,f127]) ).
thf(f127,plain,
x = y,
inference(subsumption_resolution,[],[f126,f35]) ).
thf(f35,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true,
inference(cnf_transformation,[],[f23]) ).
thf(f23,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true,
inference(flattening,[],[f12]) ).
thf(f12,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true,
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y),
inference(rectify,[],[f8]) ).
thf(f8,negated_conjecture,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y),
inference(negated_conjecture,[],[f7]) ).
thf(f7,conjecture,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz20c) ).
thf(f126,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true )
| ( x = y ) ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f122,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true )
| ( x = y ) ),
inference(superposition,[],[f121,f37]) ).
thf(f37,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f30,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
| ( X0 = X1 ) ),
inference(flattening,[],[f29]) ).
thf(f29,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ) ),
inference(flattening,[],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X1: nat,X2: nat] :
( ( X1 != X2 )
=> ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a) ).
thf(f121,plain,
$true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f117,plain,
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) ) ),
inference(superposition,[],[f111,f43]) ).
thf(f111,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X2) ) ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f110,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X2) ) ),
inference(superposition,[],[f39,f42]) ).
thf(f42,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f34,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
thf(f39,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f43,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) = $true,
inference(fool_elimination,[],[f21]) ).
thf(f21,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35 % Computer : n026.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri May 3 15:19:38 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % (16176)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36 % (16179)WARNING: value z3 for option sas not known
% 0.12/0.37 % (16180)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37 % (16181)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)
% 0.12/0.37 % (16179)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)
% 0.12/0.37 % (16183)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)
% 0.12/0.37 % Exception at run slice level% (16178)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.37
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 % (16182)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)
% 0.12/0.37 % (16177)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37 % (16183)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37 % Exception at run slice level
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 % Exception at run slice level
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 % (16179)First to succeed.
% 0.12/0.37 % (16183)Also succeeded, but the first one will report.
% 0.12/0.37 % (16179)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16176"
% 0.12/0.37 % (16179)Refutation found. Thanks to Tanya!
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.37 % (16179)------------------------------
% 0.12/0.37 % (16179)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.37 % (16179)Termination reason: Refutation
% 0.12/0.37
% 0.12/0.37 % (16179)Memory used [KB]: 774
% 0.12/0.37 % (16179)Time elapsed: 0.006 s
% 0.12/0.37 % (16179)Instructions burned: 10 (million)
% 0.12/0.37 % (16176)Success in time 0.018 s
%------------------------------------------------------------------------------