%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG253^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 6.24s 2.73s
% Output : Refutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 20 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 114 ( 2 ~; 0 |; 0 &; 76 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
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(push_decl,type,
push: term > subst > subst ).
thf(var_decl,type,
var: term > $o ).
thf(induction2lem_decl,type,
induction2lem: $o ).
thf(induction2_lthm_decl,type,
induction2_lthm: $o ).
thf(induction2_decl,type,
induction2: $o ).
thf(axvarid_decl,type,
axvarid: $o ).
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(induction2_lthm_def,definition,
( induction2_lthm
= ( axvarid
=> ( induction2lem
=> induction2 ) ) ) ).
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(axvarid_def,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf(1,conjecture,
induction2_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ induction2_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG253^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.19 % Computer : n002.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:35:22 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.15/1.15 % [INFO] Parsing done (376ms).
% 2.15/1.16 % [INFO] Running in sequential loop mode.
% 3.06/1.55 % [INFO] eprover registered as external prover.
% 3.06/1.55 % [INFO] Scanning for conjecture ...
% 4.51/2.03 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 4.51/2.06 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 4.51/2.06 % [INFO] Problem is higher-order (TPTP THF).
% 4.51/2.06 % [INFO] Type checking passed.
% 4.51/2.07 % [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 ...
% 6.24/2.73 % External prover 'e' found a proof!
% 6.24/2.73 % [INFO] Killing All external provers ...
% 6.24/2.73 % Time passed: 2397ms (effective reasoning time: 1563ms)
% 6.24/2.73 % 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)>
% 6.24/2.73 % Axioms used in derivation (0):
% 6.24/2.73 % No. of inferences in proof: 4
% 6.24/2.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2397 ms resp. 1563 ms w/o parsing
% 6.24/2.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.24/2.77 % [INFO] Killing All external provers ...
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