TSTP Solution File: ALG258^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG258^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n028.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 May 20 18:20:25 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 29
% Syntax : Number of formulae : 119 ( 91 unt; 22 typ; 0 def)
% Number of atoms : 529 ( 236 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1611 ( 11 ~; 4 |; 0 &;1316 @)
% ( 0 <=>; 84 =>; 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 : 365 ( 260 ^ 105 !; 0 ?; 365 :)
% 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(f661,plain,
$false,
inference(trivial_inequality_removal,[],[f660]) ).
thf(f660,plain,
( ( sK1 @ sK4 @ sK3 )
!= ( sK1 @ sK4 @ sK3 ) ),
inference(superposition,[],[f577,f627]) ).
thf(f627,plain,
! [X0: term,X1: subst] :
( ( sK1 @ X1 @ X0 )
= ( sK2 @ X1 @ X0 ) ),
inference(superposition,[],[f587,f615]) ).
thf(f615,plain,
! [X0: term,X1: subst] :
( ( sub @ ( sK1 @ sh @ one ) @ ( push @ X0 @ X1 ) )
= ( sK2 @ X1 @ X0 ) ),
inference(superposition,[],[f611,f582]) ).
thf(f582,plain,
( ( sK2 @ sh @ one )
= ( sK1 @ sh @ one ) ),
inference(equality_resolution,[],[f580]) ).
thf(f580,plain,
! [X0: term] :
( ( ( lam @ X0 )
!= ( lam @ ( sK1 @ sh @ one ) ) )
| ( ( sK2 @ sh @ one )
= X0 ) ),
inference(superposition,[],[f547,f572]) ).
thf(f572,plain,
( ( lam @ ( sK2 @ sh @ one ) )
= ( lam @ ( sK1 @ sh @ one ) ) ),
inference(equality_proxy_clausification,[],[f571]) ).
thf(f571,plain,
( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( sK2 @ sh @ one ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f561]) ).
thf(f561,plain,
( $false
= ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( sK2 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ Y1 @ Y0 )
= ( sK1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f560,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) )
= ( sub @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( sK2 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ Y1 @ Y0 )
= ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f559]) ).
thf(f559,plain,
( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( Y0 @ Y2 @ Y1 )
= ( sK1 @ Y2 @ Y1 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f550]) ).
thf(f550,plain,
( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( Y0 @ Y2 @ Y1 )
= ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f549]) ).
thf(f549,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) )
= ( sub @ ( sK1 @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( ( ( lam @ ( sK1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( Y0 @ Y2 @ Y1 )
= ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f548]) ).
thf(f548,plain,
( $false
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[],[f539]) ).
thf(f539,plain,
( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f532]) ).
thf(f532,plain,
( ( ( !! @ 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] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f525]) ).
thf(f525,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ 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] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f524]) ).
thf(f524,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ 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] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[],[f523]) ).
thf(f523,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ 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] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ 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] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f387,f498]) ).
thf(f498,plain,
( hoaslaminj_lthm
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ 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] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ 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] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f444,f409,f427,f424,f453]) ).
thf(f453,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ 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] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f417,f441,f441]) ).
thf(f441,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f185]) ).
thf(f185,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f184]) ).
thf(f184,plain,
( hoaslam
= ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( hoaslam
= ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam) ).
thf(f417,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ 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] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f269]) ).
thf(f269,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y1 @ Y4 @ Y3 ) @ 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] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f268]) ).
thf(f268,plain,
! [X0: subst > term > term] :
( ( ! [X1: subst,X2: term,X3: subst] :
( ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) )
= ( sub @ ( X0 @ X1 @ X2 ) @ X3 ) )
=> ! [X4: subst > term > term] :
( ! [X5: subst,X6: term,X7: subst] :
( ( X4 @ ( comp @ X5 @ X7 ) @ ( sub @ X6 @ X7 ) )
= ( sub @ ( X4 @ X5 @ X6 ) @ X7 ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: subst,X13: term] :
( ( X4 @ X12 @ X13 )
= ( X0 @ X12 @ X13 ) ) ) ) )
= hoaslaminj ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X10: subst > term > term] :
( ( ! [X2: subst,X0: term,X3: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X11: subst > term > term] :
( ! [X2: subst,X0: term,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 ) ) ) ) )
= hoaslaminj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj) ).
thf(f424,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f271]) ).
thf(f271,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f270]) ).
thf(f270,plain,
( laminj
= ( ! [X0: term,X1: term] :
( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
( laminj
= ( ! [X1: term,X0: term] :
( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj) ).
thf(f427,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f172]) ).
thf(f172,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f171]) ).
thf(f171,plain,
! [X0: term,X1: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 )
= axshiftcons ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X0: term,X2: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 )
= axshiftcons ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons) ).
thf(f409,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f293]) ).
thf(f293,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f292]) ).
thf(f292,plain,
! [X0: term,X1: subst] :
( ( ( sub @ one @ ( push @ X0 @ X1 ) )
= X0 )
= axvarcons ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: term,X2: subst] :
( ( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 )
= axvarcons ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons) ).
thf(f444,plain,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
inference(cnf_transformation,[],[f273]) ).
thf(f273,plain,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
inference(fool_elimination,[],[f272]) ).
thf(f272,plain,
( ( hoaslaminj_lthm = axvarcons )
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ),
inference(rectify,[],[f66]) ).
thf(f66,axiom,
( ( hoaslaminj_lthm = axvarcons )
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_lthm) ).
thf(f387,plain,
hoaslaminj_lthm != $true,
inference(cnf_transformation,[],[f331]) ).
thf(f331,plain,
hoaslaminj_lthm != $true,
inference(flattening,[],[f327]) ).
thf(f327,plain,
hoaslaminj_lthm != $true,
inference(fool_elimination,[],[f326]) ).
thf(f326,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(f547,plain,
! [X2: term,X1: term] :
( ( ( lam @ X1 )
!= ( lam @ X2 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f546]) ).
thf(f546,plain,
! [X2: term,X1: term] :
( ( X1 = X2 )
| ( $false
= ( ( lam @ X2 )
= ( lam @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f545]) ).
thf(f545,plain,
! [X2: term,X1: term] :
( ( ( X2 = X1 )
= $true )
| ( $false
= ( ( lam @ X2 )
= ( lam @ X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f544]) ).
thf(f544,plain,
! [X2: term,X1: term] :
( ( ( ( lam @ X2 )
= ( lam @ X1 ) )
=> ( X2 = X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f543]) ).
thf(f543,plain,
! [X2: term,X1: term] :
( ( ^ [Y0: term] :
( ( ( lam @ Y0 )
= ( lam @ X1 ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f542]) ).
thf(f542,plain,
! [X1: term] :
( ( !! @ term
@ ^ [Y0: term] :
( ( ( lam @ Y0 )
= ( lam @ X1 ) )
=> ( Y0 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f541]) ).
thf(f541,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f540]) ).
thf(f540,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f532]) ).
thf(f611,plain,
! [X0: term,X1: subst] :
( ( sub @ ( sK2 @ sh @ one ) @ ( push @ X0 @ X1 ) )
= ( sK2 @ X1 @ X0 ) ),
inference(superposition,[],[f585,f538]) ).
thf(f538,plain,
! [X2: term,X1: subst] :
( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[],[f537]) ).
thf(f537,plain,
! [X2: term,X1: subst] :
( ( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f536]) ).
thf(f536,plain,
! [X2: term,X1: subst] :
( ( ^ [Y0: term] :
( ( comp @ sh @ ( push @ Y0 @ X1 ) )
= X1 )
@ X2 )
= $true ),
inference(pi_clausification,[],[f535]) ).
thf(f535,plain,
! [X1: subst] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( comp @ sh @ ( push @ Y0 @ X1 ) )
= X1 ) ) ),
inference(beta_eta_normalization,[],[f534]) ).
thf(f534,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f533]) ).
thf(f533,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f525]) ).
thf(f585,plain,
! [X2: subst,X0: term,X1: subst] :
( ( sub @ ( sK2 @ X2 @ one ) @ ( push @ X0 @ X1 ) )
= ( sK2 @ ( comp @ X2 @ ( push @ X0 @ X1 ) ) @ X0 ) ),
inference(superposition,[],[f569,f531]) ).
thf(f531,plain,
! [X2: term,X1: subst] :
( ( sub @ one @ ( push @ X2 @ X1 ) )
= X2 ),
inference(equality_proxy_clausification,[],[f530]) ).
thf(f530,plain,
! [X2: term,X1: subst] :
( ( ( sub @ one @ ( push @ X2 @ X1 ) )
= X2 )
= $true ),
inference(beta_eta_normalization,[],[f529]) ).
thf(f529,plain,
! [X2: term,X1: subst] :
( ( ^ [Y0: term] :
( ( sub @ one @ ( push @ Y0 @ X1 ) )
= Y0 )
@ X2 )
= $true ),
inference(pi_clausification,[],[f528]) ).
thf(f528,plain,
! [X1: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ one @ ( push @ Y0 @ X1 ) )
= Y0 ) )
= $true ),
inference(beta_eta_normalization,[],[f527]) ).
thf(f527,plain,
! [X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) )
@ X1 ) ),
inference(pi_clausification,[],[f526]) ).
thf(f526,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f524]) ).
thf(f569,plain,
! [X2: term,X3: subst,X1: subst] :
( ( sub @ ( sK2 @ X3 @ X2 ) @ X1 )
= ( sK2 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f568]) ).
thf(f568,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ( sK2 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) )
= ( sub @ ( sK2 @ X3 @ X2 ) @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f567]) ).
thf(f567,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ^ [Y0: subst] :
( ( sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) )
= ( sub @ ( sK2 @ Y0 @ X2 ) @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f566]) ).
thf(f566,plain,
! [X2: term,X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( ( sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) )
= ( sub @ ( sK2 @ Y0 @ X2 ) @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f565]) ).
thf(f565,plain,
! [X2: term,X1: subst] :
( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ ( comp @ Y1 @ X1 ) @ ( sub @ Y0 @ X1 ) )
= ( sub @ ( sK2 @ Y1 @ Y0 ) @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f564]) ).
thf(f564,plain,
! [X1: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ ( comp @ Y1 @ X1 ) @ ( sub @ Y0 @ X1 ) )
= ( sub @ ( sK2 @ Y1 @ Y0 ) @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f563]) ).
thf(f563,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) )
= ( sub @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f562]) ).
thf(f562,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) )
= ( sub @ ( sK2 @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f587,plain,
! [X0: term,X1: subst] :
( ( sub @ ( sK1 @ sh @ one ) @ ( push @ X0 @ X1 ) )
= ( sK1 @ X1 @ X0 ) ),
inference(superposition,[],[f583,f538]) ).
thf(f583,plain,
! [X2: subst,X0: term,X1: subst] :
( ( sK1 @ ( comp @ X2 @ ( push @ X0 @ X1 ) ) @ X0 )
= ( sub @ ( sK1 @ X2 @ one ) @ ( push @ X0 @ X1 ) ) ),
inference(superposition,[],[f558,f531]) ).
thf(f558,plain,
! [X2: term,X3: subst,X1: subst] :
( ( sub @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f557]) ).
thf(f557,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ( sK1 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) )
= ( sub @ ( sK1 @ X3 @ X2 ) @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f556]) ).
thf(f556,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ^ [Y0: subst] :
( ( sK1 @ ( comp @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) )
= ( sub @ ( sK1 @ Y0 @ X2 ) @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f555]) ).
thf(f555,plain,
! [X2: term,X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( ( sK1 @ ( comp @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) )
= ( sub @ ( sK1 @ Y0 @ X2 ) @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f554]) ).
thf(f554,plain,
! [X2: term,X1: subst] :
( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK1 @ ( comp @ Y1 @ X1 ) @ ( sub @ Y0 @ X1 ) )
= ( sub @ ( sK1 @ Y1 @ Y0 ) @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f553]) ).
thf(f553,plain,
! [X1: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK1 @ ( comp @ Y1 @ X1 ) @ ( sub @ Y0 @ X1 ) )
= ( sub @ ( sK1 @ Y1 @ Y0 ) @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f552]) ).
thf(f552,plain,
! [X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) )
= ( sub @ ( sK1 @ Y2 @ Y1 ) @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f551]) ).
thf(f551,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) )
= ( sub @ ( sK1 @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f549]) ).
thf(f577,plain,
( ( sK1 @ sK4 @ sK3 )
!= ( sK2 @ sK4 @ sK3 ) ),
inference(equality_proxy_clausification,[],[f576]) ).
thf(f576,plain,
( ( ( sK2 @ sK4 @ sK3 )
= ( sK1 @ sK4 @ sK3 ) )
= $false ),
inference(beta_eta_normalization,[],[f575]) ).
thf(f575,plain,
( ( ^ [Y0: subst] :
( ( sK2 @ Y0 @ sK3 )
= ( sK1 @ Y0 @ sK3 ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f574]) ).
thf(f574,plain,
( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sK2 @ Y0 @ sK3 )
= ( sK1 @ Y0 @ sK3 ) ) ) ),
inference(beta_eta_normalization,[],[f573]) ).
thf(f573,plain,
( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ Y1 @ Y0 )
= ( sK1 @ Y1 @ Y0 ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f570]) ).
thf(f570,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ Y1 @ Y0 )
= ( sK1 @ Y1 @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f561]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ALG258^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.08/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 22:54:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.38 % (5490)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (5492)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)
% 0.15/0.38 % (5491)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)
% 0.15/0.38 % (5493)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (5495)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)
% 0.15/0.38 % (5494)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)
% 0.15/0.38 % (5496)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (5497)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)
% 0.15/0.38 % (5493)Instruction limit reached!
% 0.15/0.38 % (5493)------------------------------
% 0.15/0.38 % (5493)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (5493)Termination reason: Unknown
% 0.15/0.39 % (5494)Instruction limit reached!
% 0.15/0.39 % (5494)------------------------------
% 0.15/0.39 % (5494)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (5493)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (5493)Memory used [KB]: 1279
% 0.15/0.39 % (5493)Time elapsed: 0.004 s
% 0.15/0.39 % (5493)Instructions burned: 3 (million)
% 0.15/0.39 % (5493)------------------------------
% 0.15/0.39 % (5493)------------------------------
% 0.15/0.39 % (5494)Termination reason: Unknown
% 0.15/0.39 % (5494)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (5494)Memory used [KB]: 1279
% 0.15/0.39 % (5494)Time elapsed: 0.004 s
% 0.15/0.39 % (5494)Instructions burned: 3 (million)
% 0.15/0.39 % (5494)------------------------------
% 0.15/0.39 % (5494)------------------------------
% 0.15/0.39 % (5497)Instruction limit reached!
% 0.15/0.39 % (5497)------------------------------
% 0.15/0.39 % (5497)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (5497)Termination reason: Unknown
% 0.15/0.39 % (5497)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (5497)Memory used [KB]: 1279
% 0.15/0.39 % (5497)Time elapsed: 0.004 s
% 0.15/0.39 % (5497)Instructions burned: 3 (million)
% 0.15/0.39 % (5497)------------------------------
% 0.15/0.39 % (5497)------------------------------
% 0.15/0.39 % (5491)Instruction limit reached!
% 0.15/0.39 % (5491)------------------------------
% 0.15/0.39 % (5491)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (5491)Termination reason: Unknown
% 0.15/0.39 % (5491)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (5491)Memory used [KB]: 1279
% 0.15/0.39 % (5491)Time elapsed: 0.005 s
% 0.15/0.39 % (5491)Instructions burned: 5 (million)
% 0.15/0.39 % (5491)------------------------------
% 0.15/0.39 % (5491)------------------------------
% 0.15/0.39 % (5496)Instruction limit reached!
% 0.15/0.39 % (5496)------------------------------
% 0.15/0.39 % (5496)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (5496)Termination reason: Unknown
% 0.15/0.39 % (5496)Termination phase: Property scanning
% 0.15/0.39
% 0.15/0.39 % (5496)Memory used [KB]: 1663
% 0.15/0.39 % (5496)Time elapsed: 0.013 s
% 0.15/0.39 % (5496)Instructions burned: 18 (million)
% 0.15/0.39 % (5496)------------------------------
% 0.15/0.39 % (5496)------------------------------
% 0.15/0.40 % (5492)Instruction limit reached!
% 0.15/0.40 % (5492)------------------------------
% 0.15/0.40 % (5492)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (5492)Termination reason: Unknown
% 0.15/0.40 % (5492)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (5492)Memory used [KB]: 1791
% 0.15/0.40 % (5492)Time elapsed: 0.016 s
% 0.15/0.40 % (5492)Instructions burned: 27 (million)
% 0.15/0.40 % (5492)------------------------------
% 0.15/0.40 % (5492)------------------------------
% 0.15/0.40 % (5495)Refutation not found, incomplete strategy
% 0.15/0.40 % (5495)------------------------------
% 0.15/0.40 % (5495)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (5495)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.40
% 0.15/0.40
% 0.15/0.40 % (5495)Memory used [KB]: 6140
% 0.15/0.40 % (5495)Time elapsed: 0.017 s
% 0.15/0.40 % (5495)Instructions burned: 25 (million)
% 0.15/0.40 % (5495)------------------------------
% 0.15/0.40 % (5495)------------------------------
% 0.15/0.40 % (5498)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)
% 0.15/0.40 % (5500)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)
% 0.15/0.40 % (5499)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)
% 0.15/0.40 % (5501)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)
% 0.15/0.40 % (5500)Instruction limit reached!
% 0.15/0.40 % (5500)------------------------------
% 0.15/0.40 % (5500)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (5500)Termination reason: Unknown
% 0.22/0.40 % (5500)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (5500)Memory used [KB]: 1279
% 0.22/0.40 % (5500)Time elapsed: 0.004 s
% 0.22/0.40 % (5500)Instructions burned: 4 (million)
% 0.22/0.40 % (5500)------------------------------
% 0.22/0.40 % (5500)------------------------------
% 0.22/0.41 % (5502)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.41 % (5499)Instruction limit reached!
% 0.22/0.41 % (5499)------------------------------
% 0.22/0.41 % (5499)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (5499)Termination reason: Unknown
% 0.22/0.41 % (5499)Termination phase: Property scanning
% 0.22/0.41
% 0.22/0.41 % (5499)Memory used [KB]: 1663
% 0.22/0.41 % (5499)Time elapsed: 0.011 s
% 0.22/0.41 % (5499)Instructions burned: 15 (million)
% 0.22/0.41 % (5499)------------------------------
% 0.22/0.41 % (5499)------------------------------
% 0.22/0.41 % (5503)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.41 % (5502)Instruction limit reached!
% 0.22/0.41 % (5502)------------------------------
% 0.22/0.41 % (5502)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (5502)Termination reason: Unknown
% 0.22/0.41 % (5502)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (5502)Memory used [KB]: 1407
% 0.22/0.41 % (5502)Time elapsed: 0.006 s
% 0.22/0.41 % (5502)Instructions burned: 7 (million)
% 0.22/0.41 % (5502)------------------------------
% 0.22/0.41 % (5502)------------------------------
% 0.22/0.41 % (5504)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)
% 0.22/0.42 % (5504)Instruction limit reached!
% 0.22/0.42 % (5504)------------------------------
% 0.22/0.42 % (5504)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (5504)Termination reason: Unknown
% 0.22/0.42 % (5504)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (5504)Memory used [KB]: 1279
% 0.22/0.42 % (5504)Time elapsed: 0.004 s
% 0.22/0.42 % (5504)Instructions burned: 4 (million)
% 0.22/0.42 % (5504)------------------------------
% 0.22/0.42 % (5504)------------------------------
% 0.22/0.42 % (5505)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)
% 0.22/0.42 % (5498)Instruction limit reached!
% 0.22/0.42 % (5498)------------------------------
% 0.22/0.42 % (5498)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (5498)Termination reason: Unknown
% 0.22/0.42 % (5498)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (5498)Memory used [KB]: 1791
% 0.22/0.42 % (5498)Time elapsed: 0.020 s
% 0.22/0.42 % (5498)Instructions burned: 38 (million)
% 0.22/0.42 % (5498)------------------------------
% 0.22/0.42 % (5498)------------------------------
% 0.22/0.42 % (5505)Instruction limit reached!
% 0.22/0.42 % (5505)------------------------------
% 0.22/0.42 % (5505)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (5505)Termination reason: Unknown
% 0.22/0.42 % (5505)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (5505)Memory used [KB]: 1279
% 0.22/0.42 % (5505)Time elapsed: 0.004 s
% 0.22/0.42 % (5505)Instructions burned: 3 (million)
% 0.22/0.42 % (5505)------------------------------
% 0.22/0.42 % (5505)------------------------------
% 0.22/0.42 % (5503)Instruction limit reached!
% 0.22/0.42 % (5503)------------------------------
% 0.22/0.42 % (5503)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (5503)Termination reason: Unknown
% 0.22/0.42 % (5503)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (5503)Memory used [KB]: 1535
% 0.22/0.42 % (5503)Time elapsed: 0.010 s
% 0.22/0.42 % (5503)Instructions burned: 16 (million)
% 0.22/0.42 % (5503)------------------------------
% 0.22/0.42 % (5503)------------------------------
% 0.22/0.42 % (5506)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.43 % (5507)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.43 % (5506)Instruction limit reached!
% 0.22/0.43 % (5506)------------------------------
% 0.22/0.43 % (5506)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (5506)Termination reason: Unknown
% 0.22/0.43 % (5506)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (5506)Memory used [KB]: 1407
% 0.22/0.43 % (5506)Time elapsed: 0.006 s
% 0.22/0.43 % (5506)Instructions burned: 8 (million)
% 0.22/0.43 % (5506)------------------------------
% 0.22/0.43 % (5506)------------------------------
% 0.22/0.43 % (5507)Instruction limit reached!
% 0.22/0.43 % (5507)------------------------------
% 0.22/0.43 % (5507)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (5507)Termination reason: Unknown
% 0.22/0.43 % (5507)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (5507)Memory used [KB]: 1279
% 0.22/0.43 % (5507)Time elapsed: 0.003 s
% 0.22/0.43 % (5507)Instructions burned: 3 (million)
% 0.22/0.43 % (5507)------------------------------
% 0.22/0.43 % (5507)------------------------------
% 0.22/0.43 % (5508)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.43 % (5509)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.43 % (5508)Instruction limit reached!
% 0.22/0.43 % (5508)------------------------------
% 0.22/0.43 % (5508)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (5508)Termination reason: Unknown
% 0.22/0.43 % (5508)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (5508)Memory used [KB]: 1279
% 0.22/0.43 % (5508)Time elapsed: 0.004 s
% 0.22/0.43 % (5508)Instructions burned: 4 (million)
% 0.22/0.43 % (5508)------------------------------
% 0.22/0.43 % (5508)------------------------------
% 0.22/0.43 % (5510)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.43 % (5511)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.44 % (5511)Instruction limit reached!
% 0.22/0.44 % (5511)------------------------------
% 0.22/0.44 % (5511)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (5511)Termination reason: Unknown
% 0.22/0.44 % (5511)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (5511)Memory used [KB]: 1279
% 0.22/0.44 % (5511)Time elapsed: 0.006 s
% 0.22/0.44 % (5511)Instructions burned: 7 (million)
% 0.22/0.44 % (5511)------------------------------
% 0.22/0.44 % (5511)------------------------------
% 0.22/0.44 % (5509)Instruction limit reached!
% 0.22/0.44 % (5509)------------------------------
% 0.22/0.44 % (5509)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (5509)Termination reason: Unknown
% 0.22/0.44 % (5509)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (5509)Memory used [KB]: 1535
% 0.22/0.44 % (5509)Time elapsed: 0.011 s
% 0.22/0.44 % (5509)Instructions burned: 18 (million)
% 0.22/0.44 % (5509)------------------------------
% 0.22/0.44 % (5509)------------------------------
% 0.22/0.44 % (5512)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.44 % (5513)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.44 % (5490)First to succeed.
% 0.22/0.45 % (5514)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.45 % (5510)Refutation not found, incomplete strategy
% 0.22/0.45 % (5510)------------------------------
% 0.22/0.45 % (5510)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (5510)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 % (5510)Memory used [KB]: 6140
% 0.22/0.45 % (5510)Time elapsed: 0.017 s
% 0.22/0.45 % (5510)Instructions burned: 26 (million)
% 0.22/0.45 % (5510)------------------------------
% 0.22/0.45 % (5510)------------------------------
% 0.22/0.45 % (5514)Instruction limit reached!
% 0.22/0.45 % (5514)------------------------------
% 0.22/0.45 % (5514)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (5514)Termination reason: Unknown
% 0.22/0.45 % (5514)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (5514)Memory used [KB]: 1279
% 0.22/0.45 % (5514)Time elapsed: 0.005 s
% 0.22/0.45 % (5514)Instructions burned: 5 (million)
% 0.22/0.45 % (5514)------------------------------
% 0.22/0.45 % (5514)------------------------------
% 0.22/0.45 % (5490)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (5490)------------------------------
% 0.22/0.45 % (5490)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (5490)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (5490)Memory used [KB]: 6908
% 0.22/0.45 % (5490)Time elapsed: 0.069 s
% 0.22/0.45 % (5490)Instructions burned: 121 (million)
% 0.22/0.45 % (5490)------------------------------
% 0.22/0.45 % (5490)------------------------------
% 0.22/0.45 % (5489)Success in time 0.09 s
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------