%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG247^2 : 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 : n003.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 07:45:01 AM UTC 2026
% Result : Theorem 6.63s 3.02s
% Output : Refutation 7.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 7 def)
% Number of atoms : 29 ( 15 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 64 ( 8 ~; 0 |; 0 &; 56 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 30 ( 5 ^; 16 !; 5 ?; 30 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% 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(pushprop_lem0_decl,type,
pushprop_lem0: $o ).
thf(pushprop_lem0_lthm_decl,type,
pushprop_lem0_lthm: $o ).
thf(pushprop_p_and_p_prime_decl,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(sk1_decl,type,
sk1: term > $o ).
thf(sk2_decl,type,
sk2: term ).
thf(sk3_decl,type,
sk3: subst ).
thf(sk4_decl,type,
sk4: ( term > $o ) > term ).
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_lem0_lthm_def,definition,
pushprop_lem0_lthm = pushprop_lem0 ).
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(sk1_def,definition,
( sk1
= ( @+[A: term > $o] :
~ ! [B: term,C: subst] :
? [D: term > $o] :
! [E: term] :
( ( D @ E )
= ( A @ ( sub @ E @ ( push @ B @ C ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: term] :
~ ! [B: subst] :
? [C: term > $o] :
! [D: term] :
( ( C @ D )
= ( sk1 @ ( sub @ D @ ( push @ A @ B ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: subst] :
~ ? [B: term > $o] :
! [C: term] :
( ( B @ C )
= ( sk1 @ ( sub @ C @ ( push @ sk2 @ A ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: term > $o] :
@+[B: term] :
( ( A @ B )
!= ( sk1 @ ( sub @ B @ ( push @ sk2 @ sk3 ) ) ) ) ) ) ).
thf(1,conjecture,
pushprop_lem0_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ pushprop_lem0_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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: term > $o] :
( ( A @ ( sk4 @ A ) )
!= ( sk1 @ ( sub @ ( sk4 @ A ) @ ( push @ sk2 @ sk3 ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: term > $o] :
( ( A @ ( sk4 @ A ) )
!= ( sk1 @ ( sub @ ( sk4 @ A ) @ ( push @ sk2 @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
$false,
inference(pre_uni,[status(thm)],[5:[bind(A,$thf( ^ [B: term] : ( sk1 @ ( sub @ B @ ( push @ sk2 @ sk3 ) ) ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG247^2 : 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
% 0.12/0.24 % Computer : n003.cluster.edu
% 0.12/0.24 % Model : x86_64 x86_64
% 0.12/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.24 % Memory : 8046.5625MB
% 0.12/0.24 % OS : Linux 6.8.0-71-generic
% 0.12/0.24 % CPULimit : 300
% 0.12/0.24 % WCLimit : 300
% 0.12/0.24 % DateTime : Tue Sep 29 17:33:43 UTC 2026
% 0.12/0.25 % CPUTime :
% 0.12/0.25 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
% 1.07/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.31/1.40 % [INFO] Parsing done (504ms).
% 2.68/1.42 % [INFO] Running in sequential loop mode.
% 3.68/1.89 % [INFO] eprover registered as external prover.
% 3.68/1.90 % [INFO] Scanning for conjecture ...
% 5.39/2.42 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 5.39/2.45 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 5.39/2.45 % [INFO] Problem is higher-order (TPTP THF).
% 5.39/2.45 % [INFO] Type checking passed.
% 5.39/2.45 % [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 ...
% 6.63/3.02 % [INFO] Killing All external provers ...
% 6.63/3.02 % Time passed: 2571ms (effective reasoning time: 1590ms)
% 6.63/3.02 % 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)>
% 6.63/3.02 % Axioms used in derivation (0):
% 6.63/3.02 % No. of inferences in proof: 6
% 6.63/3.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2571 ms resp. 1590 ms w/o parsing
% 7.06/3.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.06/3.07 % [INFO] Killing All external provers ...
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