%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM020^1 : 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 : n026.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 4.37s 2.13s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 9 ( 8 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 49 ( 4 ~; 0 |; 0 &; 45 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-4 aty)
% Number of variables : 24 ( 19 ^; 2 !; 3 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(three_decl,type,
three: ( $i > $i ) > $i > $i ).
thf(six_decl,type,
six: ( $i > $i ) > $i > $i ).
thf(mult_decl,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(three_def,definition,
( three
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ B ) ) ) ) ) ).
thf(six_def,definition,
( six
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ) ) ).
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 @ three )
= six ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $i ) > $i > $i] :
( ( mult @ A @ three )
= six ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $i ) > $i > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : ( B @ ( B @ ( B @ C ) ) ) ) )
= ( ^ [B: $i > $i,C: $i] : ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $i ) > $i > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : ( B @ ( B @ ( B @ C ) ) ) ) )
!= ( ^ [B: $i > $i,C: $i] : ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $i ) > $i > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : ( B @ ( B @ ( B @ C ) ) ) ) )
!= ( ^ [B: $i > $i,C: $i] : ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
$false,
inference(pre_uni,[status(thm)],[5:[bind(A,$thf( ^ [B: $i > $i] : ^ [C: $i] : ( B @ ( B @ C ) ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM020^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.21 % Computer : n026.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 11:56:57 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.80/0.56 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.05/0.78 % [INFO] Parsing done (208ms).
% 1.05/0.79 % [INFO] Running in sequential loop mode.
% 1.98/1.21 % [INFO] eprover registered as external prover.
% 1.98/1.21 % [INFO] Scanning for conjecture ...
% 2.17/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.17/1.37 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.17/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.17/1.37 % [INFO] Type checking passed.
% 2.17/1.38 % [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 ...
% 4.11/2.13 % [INFO] Killing All external provers ...
% 4.11/2.13 % Time passed: 1826ms (effective reasoning time: 1331ms)
% 4.11/2.13 % 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)>
% 4.37/2.13 % Axioms used in derivation (0):
% 4.37/2.13 % No. of inferences in proof: 6
% 4.37/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1826 ms resp. 1331 ms w/o parsing
% 4.37/2.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.37/2.18 % [INFO] Killing All external provers ...
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