%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG255^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:03 AM UTC 2026
% Result : Theorem 6.85s 3.02s
% Output : Refutation 7.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of formulae : 33 ( 32 unt; 0 typ; 29 def)
% Number of atoms : 165 ( 81 equ; 0 cnn)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 508 ( 8 ~; 0 |; 6 &; 366 @)
% ( 0 <=>; 128 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 38 usr; 33 con; 0-2 aty)
% Number of variables : 158 ( 0 ^; 158 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(one_decl,type,
one: term ).
thf(ap_decl,type,
ap: term > term > term ).
thf(lam_decl,type,
lam: term > term ).
thf(sub_decl,type,
sub: term > subst > term ).
thf(id_decl,type,
id: subst ).
thf(sh_decl,type,
sh: subst ).
thf(push_decl,type,
push: term > subst > subst ).
thf(comp_decl,type,
comp: subst > subst > subst ).
thf(var_decl,type,
var: term > $o ).
thf(axmap_decl,type,
axmap: $o ).
thf(shinj_decl,type,
shinj: $o ).
thf(induction2lem_decl,type,
induction2lem: $o ).
thf(axvarshift_decl,type,
axvarshift: $o ).
thf(ulamvar1_decl,type,
ulamvar1: $o ).
thf(apnotvar_decl,type,
apnotvar: $o ).
thf(axapp_decl,type,
axapp: $o ).
thf(ulamvarind_decl,type,
ulamvarind: $o ).
thf(induction_decl,type,
induction: $o ).
thf(termmset_gthm_decl,type,
termmset_gthm: $o ).
thf(axclos_decl,type,
axclos: $o ).
thf(axassoc_decl,type,
axassoc: $o ).
thf(apinj2_decl,type,
apinj2: $o ).
thf(apinj1_decl,type,
apinj1: $o ).
thf(axvarcons_decl,type,
axvarcons: $o ).
thf(axscons_decl,type,
axscons: $o ).
thf(axidr_decl,type,
axidr: $o ).
thf(laminj_decl,type,
laminj: $o ).
thf(axabs_decl,type,
axabs: $o ).
thf(lamnotap_decl,type,
lamnotap: $o ).
thf(axidl_decl,type,
axidl: $o ).
thf(pushprop_decl,type,
pushprop: $o ).
thf(substmonoid_decl,type,
substmonoid: $o ).
thf(lamnotvar_decl,type,
lamnotvar: $o ).
thf(ulamvarsh_decl,type,
ulamvarsh: $o ).
thf(induction2_decl,type,
induction2: $o ).
thf(axshiftcons_decl,type,
axshiftcons: $o ).
thf(termmset_decl,type,
termmset: $o ).
thf(axvarid_decl,type,
axvarid: $o ).
thf(axmap_def,definition,
( axmap
= ( ! [A: term,B: subst,C: subst] :
( ( comp @ ( push @ A @ B ) @ C )
= ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) ) ) ) ).
thf(shinj_def,definition,
( shinj
= ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) ) ) ).
thf(induction2lem_def,definition,
( induction2lem
= ( ! [A: term > $o] :
( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( A @ ( sub @ B @ C ) ) ) ) ) ) ) ).
thf(axvarshift_def,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf(ulamvar1_def,definition,
( ulamvar1
= ( var @ one ) ) ).
thf(apnotvar_def,definition,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ) ).
thf(axapp_def,definition,
( axapp
= ( ! [A: term,B: term,C: subst] :
( ( sub @ ( ap @ A @ B ) @ C )
= ( ap @ ( sub @ A @ C ) @ ( sub @ B @ C ) ) ) ) ) ).
thf(ulamvarind_def,definition,
( ulamvarind
= ( ! [A: term > $o] :
( ( A @ one )
=> ( ! [B: term] :
( ( var @ B )
=> ( ( A @ B )
=> ( A @ ( sub @ B @ sh ) ) ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ B ) ) ) ) ) ) ).
thf(induction_def,definition,
( induction
= ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ( A @ B )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) ) ) ) ).
thf(termmset_gthm_def,definition,
( termmset_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(axclos_def,definition,
( axclos
= ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) ) ) ) ).
thf(axassoc_def,definition,
( axassoc
= ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) ) ) ) ).
thf(apinj2_def,definition,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ) ).
thf(apinj1_def,definition,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ) ).
thf(axvarcons_def,definition,
( axvarcons
= ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A ) ) ) ).
thf(axscons_def,definition,
( axscons
= ( ! [A: subst] :
( ( push @ ( sub @ one @ A ) @ ( comp @ sh @ A ) )
= A ) ) ) ).
thf(axidr_def,definition,
( axidr
= ( ! [A: subst] :
( ( comp @ A @ id )
= A ) ) ) ).
thf(laminj_def,definition,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ) ).
thf(axabs_def,definition,
( axabs
= ( ! [A: term,B: subst] :
( ( sub @ ( lam @ A ) @ B )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ B @ sh ) ) ) ) ) ) ) ).
thf(lamnotap_def,definition,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ) ).
thf(axidl_def,definition,
( axidl
= ( ! [A: subst] :
( ( comp @ id @ A )
= A ) ) ) ).
thf(pushprop_def,definition,
( pushprop
= ( ! [A: term > $o,B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( ( A @ B )
=> ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ ( push @ B @ C ) ) ) ) ) ) ) ) ).
thf(substmonoid_def,definition,
( substmonoid
= ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
& ! [A: subst] :
( ( comp @ id @ A )
= A )
& ! [A: subst] :
( ( comp @ A @ id )
= A ) ) ) ).
thf(lamnotvar_def,definition,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ) ).
thf(ulamvarsh_def,definition,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ) ).
thf(induction2_def,definition,
( induction2
= ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) ) ) ) ).
thf(axshiftcons_def,definition,
( axshiftcons
= ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B ) ) ) ).
thf(termmset_def,definition,
( termmset
= ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf(axvarid_def,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf(1,conjecture,
termmset_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ termmset_gthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term,B: term,C: subst] :
( ( sub @ ( ap @ A @ B ) @ C )
= ( ap @ ( sub @ A @ C ) @ ( sub @ B @ C ) ) )
=> ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A )
=> ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [A: term,B: subst] :
( ( sub @ ( lam @ A ) @ B )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ B @ sh ) ) ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ id @ A )
= A )
=> ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B )
=> ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( comp @ ( push @ A @ B ) @ C )
= ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ A @ id )
= A )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [A: subst] :
( ( push @ ( sub @ one @ A ) @ ( comp @ sh @ A ) )
= A )
=> ( ( var @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) )
=> ( ! [A: term > $o] :
( ( A @ one )
=> ( ! [B: term] :
( ( var @ B )
=> ( ( A @ B )
=> ( A @ ( sub @ B @ sh ) ) ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ B ) ) ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) )
=> ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) )
=> ( ! [A: term] :
~ ( var @ ( lam @ A ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ( A @ B )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) )
=> ( ! [A: term > $o,B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( ( A @ B )
=> ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ ( push @ B @ C ) ) ) ) ) )
=> ( ! [A: term > $o] :
( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( A @ ( sub @ B @ C ) ) ) ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) )
=> ( ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
& ! [A: subst] :
( ( comp @ id @ A )
= A )
& ! [A: subst] :
( ( comp @ A @ id )
= A ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(172,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG255^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n018.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:35:11 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.96/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.53/1.13 % [INFO] Parsing done (323ms).
% 2.01/1.14 % [INFO] Running in sequential loop mode.
% 2.94/1.53 % [INFO] eprover registered as external prover.
% 2.94/1.53 % [INFO] Scanning for conjecture ...
% 3.96/1.97 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.96/1.99 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.96/1.99 % [INFO] Problem is higher-order (TPTP THF).
% 3.96/2.00 % [INFO] Type checking passed.
% 3.96/2.00 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.85/3.02 % External prover 'e' found a proof!
% 6.85/3.02 % [INFO] Killing All external provers ...
% 6.85/3.02 % Time passed: 2661ms (effective reasoning time: 1869ms)
% 6.85/3.02 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.85/3.02 % Axioms used in derivation (0):
% 6.85/3.02 % No. of inferences in proof: 4
% 6.85/3.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2661 ms resp. 1869 ms w/o parsing
% 7.27/3.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.27/3.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------