%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG250^3 : 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 : n005.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 4.67s 1.65s
% Output : Refutation 4.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 6 unt; 0 typ; 3 def)
% Number of atoms : 17 ( 5 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 42 ( 2 ~; 0 |; 0 &; 32 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 18 ( 4 ^; 14 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(sub_decl,type,
sub: term > subst > term ).
thf(push_decl,type,
push: term > subst > subst ).
thf(var_decl,type,
var: term > $o ).
thf(pushprop_lem3v2_lthm_decl,type,
pushprop_lem3v2_lthm: $o ).
thf(pushprop_lem3v2_decl,type,
pushprop_lem3v2: $o ).
thf(pushprop_p_and_p_prime_decl,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(pushprop_lem3v2_lthm_def,definition,
pushprop_lem3v2_lthm = pushprop_lem3v2 ).
thf(pushprop_lem3v2_def,definition,
( pushprop_lem3v2
= ( ! [A: term > $o,B: term > $o,C: term,D: subst] :
( ( pushprop_p_and_p_prime @ C @ D @ A @ B )
=> ( ! [E: term] :
( ( var @ E )
=> ( B @ E ) )
=> ! [E: term] :
( ( var @ E )
=> ( A @ ( sub @ E @ ( push @ C @ D ) ) ) ) ) ) ) ) ).
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_lem3v2_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ pushprop_lem3v2_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: term > $o,B: term > $o,C: term,D: subst] :
( ! [E: term] :
( ( B @ E )
= ( A @ ( sub @ E @ ( push @ C @ D ) ) ) )
=> ( ! [E: term] :
( ( var @ E )
=> ( B @ E ) )
=> ! [E: term] :
( ( var @ E )
=> ( A @ ( sub @ E @ ( push @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG250^3 : 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
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:32:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 0.66/0.49 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/0.71 % [INFO] Parsing done (220ms).
% 1.49/0.71 % [INFO] Running in sequential loop mode.
% 2.20/0.92 % [INFO] eprover registered as external prover.
% 2.20/0.92 % [INFO] Scanning for conjecture ...
% 3.34/1.21 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.34/1.22 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.34/1.22 % [INFO] Problem is higher-order (TPTP THF).
% 3.34/1.22 % [INFO] Type checking passed.
% 3.34/1.23 % [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 ...
% 4.67/1.65 % External prover 'e' found a proof!
% 4.67/1.65 % [INFO] Killing All external provers ...
% 4.67/1.65 % Time passed: 1377ms (effective reasoning time: 931ms)
% 4.67/1.65 % 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)>
% 4.67/1.65 % Axioms used in derivation (0):
% 4.67/1.65 % No. of inferences in proof: 4
% 4.67/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1377 ms resp. 931 ms w/o parsing
% 4.67/1.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.67/1.70 % [INFO] Killing All external provers ...
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