%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG251^2 : 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 : n001.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 07:45:02 AM UTC 2026
% Result : Theorem 5.48s 2.35s
% Output : Refutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 13 ( 12 unt; 0 typ; 9 def)
% Number of atoms : 47 ( 17 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 120 ( 2 ~; 0 |; 0 &; 88 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 11 con; 0-4 aty)
% Number of variables : 44 ( 4 ^; 38 !; 2 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(one_decl,type,
one: term ).
thf(sub_decl,type,
sub: term > subst > term ).
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(ulamvar1_decl,type,
ulamvar1: $o ).
thf(ulamvarind_decl,type,
ulamvarind: $o ).
thf(axclos_decl,type,
axclos: $o ).
thf(pushprop_lthm_decl,type,
pushprop_lthm: $o ).
thf(axvarcons_decl,type,
axvarcons: $o ).
thf(pushprop_lem0_decl,type,
pushprop_lem0: $o ).
thf(pushprop_decl,type,
pushprop: $o ).
thf(axshiftcons_decl,type,
axshiftcons: $o ).
thf(pushprop_p_and_p_prime_decl,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(ulamvar1_def,definition,
( ulamvar1
= ( var @ one ) ) ).
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(axclos_def,definition,
( axclos
= ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) ) ) ) ).
thf(pushprop_lthm_def,definition,
( pushprop_lthm
= ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ) ).
thf(axvarcons_def,definition,
( axvarcons
= ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A ) ) ) ).
thf(pushprop_lem0_def,definition,
( pushprop_lem0
= ( ! [A: term > $o,B: term,C: subst] :
? [D: term > $o] : ( pushprop_p_and_p_prime @ B @ C @ A @ D ) ) ) ).
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(axshiftcons_def,definition,
( axshiftcons
= ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B ) ) ) ).
thf(pushprop_p_and_p_prime_def,definition,
( pushprop_p_and_p_prime
= ( ^ [A: term,B: subst,C: term > $o,D: term > $o] :
! [E: term] :
( ( D @ E )
= ( C @ ( sub @ E @ ( push @ A @ B ) ) ) ) ) ) ).
thf(1,conjecture,
pushprop_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ pushprop_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term > $o,B: term,C: subst] :
? [D: term > $o] :
! [E: term] :
( ( D @ E )
= ( A @ ( sub @ E @ ( push @ B @ C ) ) ) )
=> ( ( var @ one )
=> ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A )
=> ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B )
=> ( ! [A: term > $o] :
( ( A @ one )
=> ( ! [B: term] :
( ( var @ B )
=> ( ( A @ B )
=> ( A @ ( sub @ B @ sh ) ) ) )
=> ! [B: term] :
( ( var @ B )
=> ( 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 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG251^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.08 % 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
% 0.11/0.21 % Computer : n001.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 17:38:21 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.89/0.75 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/0.98 % [INFO] Parsing done (225ms).
% 1.47/0.99 % [INFO] Running in sequential loop mode.
% 2.57/1.20 % [INFO] eprover registered as external prover.
% 2.57/1.21 % [INFO] Scanning for conjecture ...
% 3.71/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 4.02/1.71 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 4.02/1.72 % [INFO] Problem is higher-order (TPTP THF).
% 4.02/1.72 % [INFO] Type checking passed.
% 4.02/1.72 % [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 ...
% 5.48/2.35 % External prover 'e' found a proof!
% 5.48/2.35 % [INFO] Killing All external provers ...
% 5.48/2.35 % Time passed: 2002ms (effective reasoning time: 1355ms)
% 5.48/2.35 % 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)>
% 5.48/2.35 % Axioms used in derivation (0):
% 5.48/2.35 % No. of inferences in proof: 4
% 5.48/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2002 ms resp. 1355 ms w/o parsing
% 5.74/2.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.74/2.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------