TSTP Solution File: ALG258^2 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : ALG258^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n023.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 : Mon Jun 24 04:08:45 EDT 2024
% Result : Theorem 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 29
% Syntax : Number of formulae : 118 ( 90 unt; 22 typ; 0 def)
% Number of atoms : 525 ( 233 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 1609 ( 12 ~; 4 |; 0 &;1314 @)
% ( 0 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 153 ( 153 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 23 usr; 13 con; 0-4 aty)
% ( 196 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 363 ( 260 ^ 103 !; 0 ?; 363 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_142,type,
sK1: subst > term > term ).
thf(func_def_143,type,
sK2: subst > term > term ).
thf(func_def_144,type,
sK3: term ).
thf(func_def_145,type,
sK4: subst ).
thf(f659,plain,
$false,
inference(trivial_inequality_removal,[],[f658]) ).
thf(f658,plain,
( ( sK1 @ sK4 @ sK3 )
!= ( sK1 @ sK4 @ sK3 ) ),
inference(superposition,[],[f575,f622]) ).
thf(f622,plain,
! [X0: term,X1: subst] :
( ( sK2 @ X1 @ X0 )
= ( sK1 @ X1 @ X0 ) ),
inference(superposition,[],[f613,f585]) ).
thf(f585,plain,
! [X0: term,X1: subst] :
( ( sK1 @ X1 @ X0 )
= ( sub @ ( sK1 @ sh @ one ) @ ( push @ X0 @ X1 ) ) ),
inference(superposition,[],[f581,f536]) ).
thf(f536,plain,
! [X2: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ),
inference(equality_proxy_clausification,[],[f535]) ).
thf(f535,plain,
! [X2: subst,X1: term] :
( ( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
= $true ),
inference(beta_eta_normalization,[],[f534]) ).
thf(f534,plain,
! [X2: subst,X1: term] :
( $true
= ( ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X1 @ Y0 ) )
= Y0 )
@ X2 ) ),
inference(pi_clausification,[],[f533]) ).
thf(f533,plain,
! [X1: term] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X1 @ Y0 ) )
= Y0 ) ) ),
inference(beta_eta_normalization,[],[f532]) ).
thf(f532,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f531]) ).
thf(f531,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f523,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f522]) ).
thf(f522,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[],[f521]) ).
thf(f521,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f404,f496]) ).
thf(f496,plain,
( hoaslaminj_lthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f418,f441,f342,f394,f451]) ).
thf(f451,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f431,f437,f437]) ).
thf(f437,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f147]) ).
thf(f147,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f146]) ).
thf(f146,plain,
( ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) )
= hoaslam ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) )
= hoaslam ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam) ).
thf(f431,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f324]) ).
thf(f324,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f323]) ).
thf(f323,plain,
( hoaslaminj
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( X0 @ X3 @ X2 ) @ X1 )
= ( X0 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) )
=> ! [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X6 @ X5 ) @ X7 )
= ( X4 @ ( comp @ X6 @ X7 ) @ ( sub @ X5 @ X7 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: subst,X13: term] :
( ( X0 @ X12 @ X13 )
= ( X4 @ X12 @ X13 ) ) ) ) ) ) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
( hoaslaminj
= ( ! [X10: subst > term > term] :
( ! [X3: subst,X0: term,X2: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X11: subst > term > term] :
( ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( X11 @ X2 @ X0 ) @ X3 )
= ( X11 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
= ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X11 @ X2 @ X0 ) ) )
=> ! [X2: subst,X0: term] :
( ( X10 @ X2 @ X0 )
= ( X11 @ X2 @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj) ).
thf(f394,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f123,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,axiom,
! [X0: term,X1: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj) ).
thf(f342,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f296,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f295]) ).
thf(f295,plain,
! [X0: subst,X1: term] :
( ( ( comp @ sh @ ( push @ X1 @ X0 ) )
= X0 )
= axshiftcons ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X2: subst,X0: term] :
( ( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 )
= axshiftcons ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons) ).
thf(f441,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f284]) ).
thf(f284,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f283]) ).
thf(f283,plain,
! [X0: subst,X1: term] :
( ( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 )
= axvarcons ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X2: subst,X0: term] :
( ( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 )
= axvarcons ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons) ).
thf(f418,plain,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
inference(cnf_transformation,[],[f137]) ).
thf(f137,plain,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f136,plain,
( axvarcons
=> ( ( axshiftcons
=> ( laminj
=> hoaslaminj ) )
= hoaslaminj_lthm ) ),
inference(rectify,[],[f66]) ).
thf(f66,axiom,
( axvarcons
=> ( ( axshiftcons
=> ( laminj
=> hoaslaminj ) )
= hoaslaminj_lthm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_lthm) ).
thf(f404,plain,
hoaslaminj_lthm != $true,
inference(cnf_transformation,[],[f329]) ).
thf(f329,plain,
hoaslaminj_lthm != $true,
inference(flattening,[],[f120]) ).
thf(f120,plain,
hoaslaminj_lthm != $true,
inference(fool_elimination,[],[f119]) ).
thf(f119,plain,
~ hoaslaminj_lthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoaslaminj_lthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoaslaminj_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f581,plain,
! [X2: subst,X0: term,X1: subst] :
( ( sub @ ( sK1 @ X2 @ one ) @ ( push @ X0 @ X1 ) )
= ( sK1 @ ( comp @ X2 @ ( push @ X0 @ X1 ) ) @ X0 ) ),
inference(superposition,[],[f556,f529]) ).
thf(f529,plain,
! [X2: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 ),
inference(equality_proxy_clausification,[],[f528]) ).
thf(f528,plain,
! [X2: subst,X1: term] :
( ( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f527]) ).
thf(f527,plain,
! [X2: subst,X1: term] :
( ( ^ [Y0: subst] :
( ( sub @ one @ ( push @ X1 @ Y0 ) )
= X1 )
@ X2 )
= $true ),
inference(pi_clausification,[],[f526]) ).
thf(f526,plain,
! [X1: term] :
( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ one @ ( push @ X1 @ Y0 ) )
= X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f525]) ).
thf(f525,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f524]) ).
thf(f524,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f522]) ).
thf(f556,plain,
! [X2: term,X3: subst,X1: subst] :
( ( sub @ ( sK1 @ X1 @ X2 ) @ X3 )
= ( sK1 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ),
inference(equality_proxy_clausification,[],[f555]) ).
thf(f555,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ( sub @ ( sK1 @ X1 @ X2 ) @ X3 )
= ( sK1 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f554]) ).
thf(f554,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ^ [Y0: subst] :
( ( sub @ ( sK1 @ X1 @ X2 ) @ Y0 )
= ( sK1 @ ( comp @ X1 @ Y0 ) @ ( sub @ X2 @ Y0 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f553]) ).
thf(f553,plain,
! [X2: term,X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK1 @ X1 @ X2 ) @ Y0 )
= ( sK1 @ ( comp @ X1 @ Y0 ) @ ( sub @ X2 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f552]) ).
thf(f552,plain,
! [X2: term,X1: subst] :
( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK1 @ X1 @ Y0 ) @ Y1 )
= ( sK1 @ ( comp @ X1 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f551]) ).
thf(f551,plain,
! [X1: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK1 @ X1 @ Y0 ) @ Y1 )
= ( sK1 @ ( comp @ X1 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f550]) ).
thf(f550,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f549]) ).
thf(f549,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f547]) ).
thf(f547,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 )
= ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) ) ) ) ) )
=> ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK1 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f546]) ).
thf(f546,plain,
( $false
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[],[f537]) ).
thf(f537,plain,
( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f530]) ).
thf(f530,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 )
= ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f613,plain,
! [X0: subst,X1: term] :
( ( sub @ ( sK1 @ sh @ one ) @ ( push @ X1 @ X0 ) )
= ( sK2 @ X0 @ X1 ) ),
inference(superposition,[],[f608,f580]) ).
thf(f580,plain,
( ( sK1 @ sh @ one )
= ( sK2 @ sh @ one ) ),
inference(equality_resolution,[],[f578]) ).
thf(f578,plain,
! [X0: term] :
( ( ( lam @ X0 )
!= ( lam @ ( sK1 @ sh @ one ) ) )
| ( ( sK2 @ sh @ one )
= X0 ) ),
inference(superposition,[],[f545,f570]) ).
thf(f570,plain,
( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( sK2 @ sh @ one ) ) ),
inference(equality_proxy_clausification,[],[f569]) ).
thf(f569,plain,
( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( sK2 @ sh @ one ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f559]) ).
thf(f559,plain,
( $false
= ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( sK2 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK1 @ Y1 @ Y0 )
= ( sK2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f558]) ).
thf(f558,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sK2 @ Y1 @ Y2 ) @ Y0 )
= ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( sK2 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK1 @ Y1 @ Y0 )
= ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f557]) ).
thf(f557,plain,
( $false
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 )
= ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) ) ) ) ) )
=> ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK1 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f548]) ).
thf(f548,plain,
( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 )
= ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) ) ) ) ) )
=> ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK1 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f547]) ).
thf(f545,plain,
! [X2: term,X1: term] :
( ( ( lam @ X1 )
!= ( lam @ X2 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f544]) ).
thf(f544,plain,
! [X2: term,X1: term] :
( ( ( X2 = X1 )
= $true )
| ( ( lam @ X1 )
!= ( lam @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f543]) ).
thf(f543,plain,
! [X2: term,X1: term] :
( ( $false
= ( ( lam @ X2 )
= ( lam @ X1 ) ) )
| ( ( X2 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[],[f542]) ).
thf(f542,plain,
! [X2: term,X1: term] :
( ( ( ( lam @ X2 )
= ( lam @ X1 ) )
=> ( X2 = X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f541]) ).
thf(f541,plain,
! [X2: term,X1: term] :
( ( ^ [Y0: term] :
( ( ( lam @ Y0 )
= ( lam @ X1 ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f540]) ).
thf(f540,plain,
! [X1: term] :
( ( !! @ term
@ ^ [Y0: term] :
( ( ( lam @ Y0 )
= ( lam @ X1 ) )
=> ( Y0 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f539]) ).
thf(f539,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f538]) ).
thf(f538,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f530]) ).
thf(f608,plain,
! [X0: term,X1: subst] :
( ( sK2 @ X1 @ X0 )
= ( sub @ ( sK2 @ sh @ one ) @ ( push @ X0 @ X1 ) ) ),
inference(superposition,[],[f583,f536]) ).
thf(f583,plain,
! [X2: subst,X0: term,X1: subst] :
( ( sK2 @ ( comp @ X2 @ ( push @ X0 @ X1 ) ) @ X0 )
= ( sub @ ( sK2 @ X2 @ one ) @ ( push @ X0 @ X1 ) ) ),
inference(superposition,[],[f567,f529]) ).
thf(f567,plain,
! [X2: subst,X3: term,X1: subst] :
( ( sK2 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( sK2 @ X2 @ X3 ) @ X1 ) ),
inference(equality_proxy_clausification,[],[f566]) ).
thf(f566,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ( sub @ ( sK2 @ X2 @ X3 ) @ X1 )
= ( sK2 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f565]) ).
thf(f565,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ^ [Y0: term] :
( ( sub @ ( sK2 @ X2 @ Y0 ) @ X1 )
= ( sK2 @ ( comp @ X2 @ X1 ) @ ( sub @ Y0 @ X1 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f564]) ).
thf(f564,plain,
! [X2: subst,X1: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ ( sK2 @ X2 @ Y0 ) @ X1 )
= ( sK2 @ ( comp @ X2 @ X1 ) @ ( sub @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f563]) ).
thf(f563,plain,
! [X2: subst,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( sK2 @ Y0 @ Y1 ) @ X1 )
= ( sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f562]) ).
thf(f562,plain,
! [X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( sK2 @ Y0 @ Y1 ) @ X1 )
= ( sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ Y1 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f561]) ).
thf(f561,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sK2 @ Y1 @ Y2 ) @ Y0 )
= ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f560]) ).
thf(f560,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sK2 @ Y1 @ Y2 ) @ Y0 )
= ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f558]) ).
thf(f575,plain,
( ( sK2 @ sK4 @ sK3 )
!= ( sK1 @ sK4 @ sK3 ) ),
inference(equality_proxy_clausification,[],[f574]) ).
thf(f574,plain,
( $false
= ( ( sK1 @ sK4 @ sK3 )
= ( sK2 @ sK4 @ sK3 ) ) ),
inference(beta_eta_normalization,[],[f573]) ).
thf(f573,plain,
( $false
= ( ^ [Y0: subst] :
( ( sK1 @ Y0 @ sK3 )
= ( sK2 @ Y0 @ sK3 ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f572]) ).
thf(f572,plain,
( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sK1 @ Y0 @ sK3 )
= ( sK2 @ Y0 @ sK3 ) ) ) ),
inference(beta_eta_normalization,[],[f571]) ).
thf(f571,plain,
( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK1 @ Y1 @ Y0 )
= ( sK2 @ Y1 @ Y0 ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f568]) ).
thf(f568,plain,
( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK1 @ Y1 @ Y0 )
= ( sK2 @ Y1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ALG258^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.08/0.13 % Command : run_vampire %s %d THM
% 0.12/0.35 % Computer : n023.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 : Wed Jun 19 15:28:24 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.37 This is a TH0_THM_EQU_NAR problem
% 0.12/0.37 Running higher-order theorem proving
% 0.12/0.37 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.40 % (4745)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.40 % (4747)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.40 % (4746)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.12/0.40 % (4742)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.12/0.40 % (4743)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.12/0.40 % (4744)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.40 % (4741)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.40 % (4745)Instruction limit reached!
% 0.12/0.40 % (4745)------------------------------
% 0.12/0.40 % (4745)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40 % (4745)Termination reason: Unknown
% 0.12/0.40 % (4745)Termination phase: shuffling
% 0.12/0.40
% 0.12/0.40 % (4745)Memory used [KB]: 1279
% 0.12/0.40 % (4745)Time elapsed: 0.004 s
% 0.12/0.40 % (4745)Instructions burned: 3 (million)
% 0.12/0.40 % (4745)------------------------------
% 0.12/0.40 % (4745)------------------------------
% 0.12/0.40 % (4742)Instruction limit reached!
% 0.12/0.40 % (4742)------------------------------
% 0.12/0.40 % (4742)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40 % (4742)Termination reason: Unknown
% 0.12/0.40 % (4742)Termination phase: shuffling
% 0.12/0.40
% 0.12/0.40 % (4742)Memory used [KB]: 1279
% 0.12/0.40 % (4742)Time elapsed: 0.004 s
% 0.12/0.40 % (4742)Instructions burned: 4 (million)
% 0.12/0.40 % (4742)------------------------------
% 0.12/0.40 % (4742)------------------------------
% 0.12/0.40 % (4744)Instruction limit reached!
% 0.12/0.40 % (4744)------------------------------
% 0.12/0.40 % (4744)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40 % (4744)Termination reason: Unknown
% 0.12/0.40 % (4744)Termination phase: shuffling
% 0.12/0.40
% 0.12/0.40 % (4744)Memory used [KB]: 1279
% 0.12/0.40 % (4744)Time elapsed: 0.004 s
% 0.12/0.40 % (4744)Instructions burned: 3 (million)
% 0.12/0.40 % (4744)------------------------------
% 0.12/0.40 % (4744)------------------------------
% 0.12/0.41 % (4747)Instruction limit reached!
% 0.12/0.41 % (4747)------------------------------
% 0.12/0.41 % (4747)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.41 % (4747)Termination reason: Unknown
% 0.12/0.41 % (4747)Termination phase: Property scanning
% 0.12/0.41
% 0.12/0.41 % (4747)Memory used [KB]: 1663
% 0.12/0.41 % (4747)Time elapsed: 0.011 s
% 0.12/0.41 % (4747)Instructions burned: 18 (million)
% 0.12/0.41 % (4747)------------------------------
% 0.12/0.41 % (4747)------------------------------
% 0.21/0.42 % (4746)Refutation not found, incomplete strategy
% 0.21/0.42 % (4746)------------------------------
% 0.21/0.42 % (4746)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (4746)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 % (4746)Memory used [KB]: 6140
% 0.21/0.42 % (4746)Time elapsed: 0.015 s
% 0.21/0.42 % (4746)Instructions burned: 24 (million)
% 0.21/0.42 % (4746)------------------------------
% 0.21/0.42 % (4746)------------------------------
% 0.21/0.42 % (4743)Instruction limit reached!
% 0.21/0.42 % (4743)------------------------------
% 0.21/0.42 % (4743)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (4743)Termination reason: Unknown
% 0.21/0.42 % (4743)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (4743)Memory used [KB]: 1791
% 0.21/0.42 % (4743)Time elapsed: 0.016 s
% 0.21/0.42 % (4743)Instructions burned: 28 (million)
% 0.21/0.42 % (4743)------------------------------
% 0.21/0.42 % (4743)------------------------------
% 0.21/0.42 % (4748)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (4750)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.42 % (4749)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.42 % (4748)Instruction limit reached!
% 0.21/0.42 % (4748)------------------------------
% 0.21/0.42 % (4748)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (4748)Termination reason: Unknown
% 0.21/0.42 % (4748)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (4748)Memory used [KB]: 1279
% 0.21/0.42 % (4748)Time elapsed: 0.004 s
% 0.21/0.42 % (4748)Instructions burned: 3 (million)
% 0.21/0.42 % (4748)------------------------------
% 0.21/0.42 % (4748)------------------------------
% 0.21/0.43 % (4751)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (4750)Instruction limit reached!
% 0.21/0.43 % (4750)------------------------------
% 0.21/0.43 % (4750)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (4750)Termination reason: Unknown
% 0.21/0.43 % (4750)Termination phase: Property scanning
% 0.21/0.43
% 0.21/0.43 % (4750)Memory used [KB]: 1663
% 0.21/0.43 % (4750)Time elapsed: 0.011 s
% 0.21/0.43 % (4750)Instructions burned: 16 (million)
% 0.21/0.43 % (4750)------------------------------
% 0.21/0.43 % (4750)------------------------------
% 0.21/0.43 % (4751)Instruction limit reached!
% 0.21/0.43 % (4751)------------------------------
% 0.21/0.43 % (4751)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (4751)Termination reason: Unknown
% 0.21/0.43 % (4751)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (4751)Memory used [KB]: 1279
% 0.21/0.43 % (4751)Time elapsed: 0.005 s
% 0.21/0.43 % (4751)Instructions burned: 4 (million)
% 0.21/0.43 % (4751)------------------------------
% 0.21/0.43 % (4751)------------------------------
% 0.21/0.43 % (4752)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.43 % (4753)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.44 % (4753)Instruction limit reached!
% 0.21/0.44 % (4753)------------------------------
% 0.21/0.44 % (4753)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.44 % (4753)Termination reason: Unknown
% 0.21/0.44 % (4753)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (4753)Memory used [KB]: 1407
% 0.21/0.44 % (4753)Time elapsed: 0.006 s
% 0.21/0.44 % (4753)Instructions burned: 7 (million)
% 0.21/0.44 % (4753)------------------------------
% 0.21/0.44 % (4753)------------------------------
% 0.21/0.44 % (4749)Instruction limit reached!
% 0.21/0.44 % (4749)------------------------------
% 0.21/0.44 % (4749)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.44 % (4749)Termination reason: Unknown
% 0.21/0.44 % (4749)Termination phase: Property scanning
% 0.21/0.44
% 0.21/0.44 % (4749)Memory used [KB]: 1791
% 0.21/0.44 % (4749)Time elapsed: 0.020 s
% 0.21/0.44 % (4749)Instructions burned: 37 (million)
% 0.21/0.44 % (4749)------------------------------
% 0.21/0.44 % (4749)------------------------------
% 0.21/0.44 % (4754)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.44 % (4741)First to succeed.
% 0.21/0.45 % (4755)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.45 % (4754)Instruction limit reached!
% 0.21/0.45 % (4754)------------------------------
% 0.21/0.45 % (4754)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.45 % (4754)Termination reason: Unknown
% 0.21/0.45 % (4756)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.45 % (4754)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (4754)Memory used [KB]: 1663
% 0.21/0.45 % (4741)Refutation found. Thanks to Tanya!
% 0.21/0.45 % SZS status Theorem for theBenchmark
% 0.21/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.45 % (4741)------------------------------
% 0.21/0.45 % (4741)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.45 % (4741)Termination reason: Refutation
% 0.21/0.45
% 0.21/0.45 % (4741)Memory used [KB]: 6908
% 0.21/0.45 % (4741)Time elapsed: 0.046 s
% 0.21/0.45 % (4741)Instructions burned: 111 (million)
% 0.21/0.45 % (4741)------------------------------
% 0.21/0.45 % (4741)------------------------------
% 0.21/0.45 % (4740)Success in time 0.069 s
%------------------------------------------------------------------------------