TSTP Solution File: NUM743^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM743^1 : 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 : n029.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 02:13:10 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 74 ( 20 unt; 15 typ; 0 def)
% Number of atoms : 470 ( 80 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 119 ( 54 ~; 44 |; 0 &; 0 @)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 21 >; 1 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-6 aty)
% Number of variables : 63 ( 0 ^ 57 !; 0 ?; 63 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
frac: $tType ).
thf(func_def_1,type,
x: frac ).
thf(func_def_2,type,
y: frac ).
thf(func_def_3,type,
z: frac ).
thf(func_def_4,type,
lessf: frac > frac > $o ).
thf(func_def_6,type,
eq: frac > frac > $o ).
thf(func_def_10,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_11,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f156,plain,
$false,
inference(avatar_sat_refutation,[],[f83,f152,f155]) ).
thf(f155,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f154]) ).
thf(f154,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f153,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f78,f96]) ).
thf(f96,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) = $false,
inference(trivial_inequality_removal,[],[f95]) ).
thf(f95,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) = $false ) ),
inference(superposition,[],[f92,f10]) ).
thf(f10,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f92,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) != $true,
inference(trivial_inequality_removal,[],[f91]) ).
thf(f91,plain,
( ( $true = $false )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) != $true ) ),
inference(superposition,[],[f71,f88]) ).
thf(f88,plain,
! [X0: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),X0) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),X0) ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f85,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),X0) )
| ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),X0) ) ),
inference(superposition,[],[f38,f40]) ).
thf(f40,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),y) = $true,
inference(cnf_transformation,[],[f24]) ).
thf(f24,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),y) = $true,
inference(fool_elimination,[],[f23]) ).
thf(f23,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),y),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f38,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X1),X2) != $true )
| ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X2) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f31,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X2) )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X1),X2) != $true )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) ) ),
inference(flattening,[],[f30]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X2) )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X1),X2) != $true )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) )
=> ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X1),X2) = $true )
=> ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X2) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X1),X2)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X2) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X1: frac,X2: frac,X3: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X1),X2)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X2),X3)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X1),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz50) ).
thf(f71,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),z) = $false,
inference(trivial_inequality_removal,[],[f70]) ).
thf(f70,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),z) = $false ) ),
inference(superposition,[],[f34,f10]) ).
thf(f34,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),z) != $true,
inference(cnf_transformation,[],[f25]) ).
thf(f25,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),z) != $true,
inference(flattening,[],[f12]) ).
thf(f12,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),z) != $true,
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),z),
inference(rectify,[],[f8]) ).
thf(f8,negated_conjecture,
~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),z),
inference(negated_conjecture,[],[f7]) ).
thf(f7,conjecture,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51b) ).
thf(f78,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f76,plain,
( spl0_1
<=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f152,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f151]) ).
thf(f151,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f146,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[],[f137,f40]) ).
thf(f137,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),y) != $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f130]) ).
thf(f130,plain,
( ( $true = $false )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,x),y) != $true )
| ~ spl0_2 ),
inference(superposition,[],[f71,f127]) ).
thf(f127,plain,
( ! [X0: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),z) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),y) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f124,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),z) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),y) ) )
| ~ spl0_2 ),
inference(superposition,[],[f102,f82]) ).
thf(f82,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,y),z) = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f80,plain,
( spl0_2
<=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,y),z) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f102,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X2) )
| ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X2) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f97,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X2) )
| ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X2) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) ) ),
inference(superposition,[],[f39,f37]) ).
thf(f37,plain,
! [X0: frac] : ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0) ),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
! [X0: frac] : ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0) ),
inference(fool_elimination,[],[f17]) ).
thf(f17,plain,
! [X0: frac] : vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X1: frac] : vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(f39,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X2) )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X3) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X2),X3) = $true )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f33,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X2),X3) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X3) != $true )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X2) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) ) ),
inference(flattening,[],[f32]) ).
thf(f32,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X2),X3) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X3) != $true )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X2) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1) )
=> ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X2) )
=> ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X3) = $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X2),X3) = $true ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f21,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X0),X1)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X2)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X3)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X2),X3) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X1),X2)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X3)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X4)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,X3),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz45) ).
thf(f83,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f35,f80,f76]) ).
thf(f35,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,y),z) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) = $true ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f28,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,y),z) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) = $true ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f26,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) != $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,y),z) = $true ) ),
inference(flattening,[],[f14]) ).
thf(f14,plain,
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z) != $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,y),z) = $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,y),z) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),lessf,y),z)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,y),z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM743^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n029.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 06:11:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (8163)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (8166)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 % (8165)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36 % (8168)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.36 % (8167)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 % (8169)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.36 % (8170)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 % (8164)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.36 % (8166)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.36 % (8167)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37
% 0.13/0.37 % (8166)First to succeed.
% 0.13/0.37 % (8169)Also succeeded, but the first one will report.
% 0.13/0.37 % (8166)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8163"
% 0.13/0.37 % (8166)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 % (8166)------------------------------
% 0.13/0.37 % (8166)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37 % (8166)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (8166)Memory used [KB]: 847
% 0.13/0.37 % (8166)Time elapsed: 0.008 s
% 0.13/0.37 % (8166)Instructions burned: 12 (million)
% 0.13/0.37 % (8163)Success in time 0.03 s
%------------------------------------------------------------------------------