%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM798^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n020.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 08:18:13 AM UTC 2026
% Result : Theorem 3.88s 2.52s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 8 ( 7 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 0 |; 0 &; 6 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-4 aty)
% Number of variables : 12 ( 7 ^; 2 !; 3 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(one_decl,type,
one: ( $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(mult_def,definition,
( mult
= ( ^ [A: ( $i > $i ) > $i > $i,B: ( $i > $i ) > $i > $i,C: $i > $i] : ( A @ ( B @ C ) ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $i ) > $i > $i] :
( ( mult @ A @ one )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $i ) > $i > $i] :
( ( mult @ A @ one )
= one ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $i ) > $i > $i] :
( A
= ( ^ [B: $i > $i] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $i ) > $i > $i] :
( A
!= ( ^ [B: $i > $i] : B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $i ) > $i > $i] :
( A
!= ( ^ [B: $i > $i] : B ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
$false,
inference(simp,[status(thm)],[5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM798^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.10 % 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
% 0.11/0.27 % Computer : n020.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 13:01:04 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 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
% 1.35/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.98/1.42 % [INFO] Parsing done (314ms).
% 1.98/1.44 % [INFO] Running in sequential loop mode.
% 2.80/2.03 % [INFO] eprover registered as external prover.
% 2.80/2.04 % [INFO] Scanning for conjecture ...
% 3.34/2.20 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.34/2.25 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.34/2.25 % [INFO] Problem is higher-order (TPTP THF).
% 3.34/2.26 % [INFO] Type checking passed.
% 3.34/2.26 % [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 ...
% 3.88/2.51 % [INFO] Killing All external provers ...
% 3.88/2.52 % Time passed: 2038ms (effective reasoning time: 1065ms)
% 3.88/2.52 % 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)>
% 3.88/2.52 % Axioms used in derivation (0):
% 3.88/2.52 % No. of inferences in proof: 6
% 3.88/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2038 ms resp. 1065 ms w/o parsing
% 4.07/2.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.07/2.60 % [INFO] Killing All external provers ...
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