TSTP Solution File: NUM750^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM750^1 : 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 : n025.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 02:13:13 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 44 ( 18 unt; 15 typ; 0 def)
% Number of atoms : 263 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 9 avg)
% Number of connectives : 34 ( 16 ~; 12 |; 0 &; 0 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 21 >; 1 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 5 con; 0-6 aty)
% Number of variables : 43 ( 0 ^ 37 !; 0 ?; 43 :)
% ( 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,
eq: frac > frac > $o ).
thf(func_def_6,type,
pf: frac > frac > frac ).
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(f97,plain,
$false,
inference(trivial_inequality_removal,[],[f90]) ).
thf(f90,plain,
$true = $false,
inference(superposition,[],[f52,f87]) ).
thf(f87,plain,
! [X0: frac] : ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),X0)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),X0)) ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f79,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),X0)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),X0)) ) ),
inference(superposition,[],[f62,f22]) ).
thf(f22,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true,
inference(fool_elimination,[],[f14]) ).
thf(f14,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(f62,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),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X0)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X2),X0)) ) ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f56,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X0)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X2),X0)) )
| ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X2) ) ),
inference(superposition,[],[f21,f20]) ).
thf(f20,plain,
! [X0: frac] : ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0) = $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: frac] : ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0) = $true ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: frac] : vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: frac] : vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(f21,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) != $true ) ),
inference(flattening,[],[f17]) ).
thf(f17,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) = $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) != $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f13,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) = $true )
=> ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) = $true )
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) = $true ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1)
=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3)
=> vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).
thf(f52,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),z)) = $false,
inference(trivial_inequality_removal,[],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),z)) = $false ) ),
inference(superposition,[],[f19,f7]) ).
thf(f7,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f19,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),z)) != $true,
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),z)) != $true,
inference(flattening,[],[f9]) ).
thf(f9,plain,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),z)) != $true,
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),z)),
inference(rectify,[],[f5]) ).
thf(f5,negated_conjecture,
~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),z)),
inference(negated_conjecture,[],[f4]) ).
thf(f4,conjecture,
vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM750^1 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n025.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 20 05:30:38 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (2010)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (2015)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.39 % (2017)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 % (2016)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/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
% 0.15/0.39 % (2015)First to succeed.
% 0.15/0.39 % (2014)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 % (2011)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.39 % (2015)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2010"
% 0.15/0.39 % (2014)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: % (2015)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (2015)------------------------------
% 0.15/0.39 % (2015)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (2015)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (2015)Memory used [KB]: 783
% 0.15/0.39 % (2015)Time elapsed: 0.005 s
% 0.15/0.39 % (2015)Instructions burned: 10 (million)
% 0.15/0.39 % (2010)Success in time 0.015 s
%------------------------------------------------------------------------------