%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM415^1 : TPTP v9.3.1. Released v3.6.0.
% 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 08:17:49 AM UTC 2026
% Result : Theorem 2.63s 1.76s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 7 def)
% Number of atoms : 11 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 45 ( 2 ~; 0 |; 0 &; 43 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 16 ( 16 ^; 0 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(one_decl,type,
one: ( $i > $i ) > $i > $i ).
thf(two_decl,type,
two: ( $i > $i ) > $i > $i ).
thf(three_decl,type,
three: ( $i > $i ) > $i > $i ).
thf(five_decl,type,
five: ( $i > $i ) > $i > $i ).
thf(seven_decl,type,
seven: ( $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(one_def,definition,
( one
= ( ^ [A: $i > $i] : A ) ) ).
thf(two_def,definition,
( two
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ B ) ) ) ) ).
thf(three_def,definition,
( three
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ B ) ) ) ) ) ).
thf(five_def,definition,
( five
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ) ).
thf(seven_def,definition,
( seven
= ( ^ [A: $i > $i,B: $i] : ( 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 @ two @ ( plus @ three @ seven ) )
= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
!= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
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
% 0.00/0.02 % Problem : NUM415^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.21 % Computer : n003.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
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 11:54:28 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.02/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.02 % [INFO] Parsing done (219ms).
% 1.51/1.03 % [INFO] Running in sequential loop mode.
% 2.09/1.42 % [INFO] eprover registered as external prover.
% 2.09/1.43 % [INFO] Scanning for conjecture ...
% 2.26/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.26/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.26/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.26/1.59 % [INFO] Type checking passed.
% 2.26/1.59 % [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 ...
% 2.63/1.75 % [INFO] Killing All external provers ...
% 2.63/1.76 % Time passed: 1401ms (effective reasoning time: 714ms)
% 2.63/1.76 % 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)>
% 2.63/1.76 % Axioms used in derivation (0):
% 2.63/1.76 % No. of inferences in proof: 4
% 2.63/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1401 ms resp. 714 ms w/o parsing
% 2.85/1.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.85/1.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------