%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM416^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n016.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 08:17:49 AM UTC 2026
% Result : Theorem 4.96s 3.14s
% Output : Refutation 5.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 8 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 43 ( 2 ~; 0 |; 0 &; 41 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 11 ( 11 ^; 0 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(five_decl,type,
five: ( $i > $i ) > $i > $i ).
thf(ten_decl,type,
ten: ( $i > $i ) > $i > $i ).
thf(plus_decl,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(mult_decl,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(five_def,definition,
( five
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ) ).
thf(ten_def,definition,
( ten
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(plus_def,definition,
( plus
= ( ^ [A: ( $i > $i ) > $i > $i,B: ( $i > $i ) > $i > $i,C: $i > $i,D: $i] : ( A @ C @ ( B @ C @ D ) ) ) ) ).
thf(mult_def,definition,
( mult
= ( ^ [A: ( $i > $i ) > $i > $i,B: ( $i > $i ) > $i > $i,C: $i > $i] : ( A @ ( B @ C ) ) ) ) ).
thf(1,conjecture,
( ( mult @ ten @ ( mult @ ten @ ten ) )
= ( mult @ ( plus @ ten @ ten ) @ ( mult @ five @ ten ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( mult @ ten @ ( mult @ ten @ ten ) )
!= ( mult @ ( plus @ ten @ ten ) @ ( mult @ five @ ten ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
$false,
inference(simp,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM416^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n016.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 12:00:19 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
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (211ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.17/1.40 % [INFO] eprover registered as external prover.
% 2.17/1.41 % [INFO] Scanning for conjecture ...
% 2.39/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.39/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.39/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.39/1.56 % [INFO] Type checking passed.
% 2.39/1.56 % [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 ...
% 4.96/3.13 % [INFO] Killing All external provers ...
% 4.96/3.14 % Time passed: 2779ms (effective reasoning time: 2121ms)
% 4.96/3.14 % 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)>
% 4.96/3.14 % Axioms used in derivation (0):
% 4.96/3.14 % No. of inferences in proof: 4
% 4.96/3.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2779 ms resp. 2121 ms w/o parsing
% 5.14/3.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.14/3.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------