%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ047^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n011.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 08:20:44 AM UTC 2026
% Result : Theorem 4.04s 2.28s
% Output : Refutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 0 equ; 0 cnn)
% Maximal formula atoms : 30 ( 22 avg)
% Number of connectives : 581 ( 2 ~; 0 |; 42 &; 492 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 18 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 4 con; 0-5 aty)
% Number of variables : 57 ( 0 ^; 54 !; 3 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(cN_decl,type,
cN: a ).
thf(cP_decl,type,
cP: a > a > a > a > b > $o ).
thf(cD_decl,type,
cD: b > b ).
thf(cS_decl,type,
cS: a ).
thf(cG_decl,type,
cG: b > b ).
thf(cW_decl,type,
cW: b > b ).
thf(cL_decl,type,
cL: b > b ).
thf(cO_decl,type,
cO: b ).
thf(1,conjecture,
( ( ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [A: b] :
( ( cP @ cS @ cN @ cS @ cN @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cS @ cN @ cS @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cS @ cN @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cN @ cS @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ A ) ) )
& ! [A: a,B: a,C: b] :
( ( cP @ cS @ A @ cS @ B @ C )
=> ( cP @ cN @ A @ cN @ B @ ( cG @ C ) ) )
& ! [A: a,B: a,C: b] :
( ( cP @ cN @ A @ cN @ B @ C )
=> ( cP @ cS @ A @ cS @ B @ ( cG @ C ) ) )
& ! [A: b] :
( ( cP @ cS @ cN @ cS @ cS @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cS @ cN @ cN @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cD @ A ) ) ) )
=> ? [A: b] : ( cP @ cN @ cN @ cN @ cN @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM100A) ).
thf(2,negated_conjecture,
~ ( ( ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [A: b] :
( ( cP @ cS @ cN @ cS @ cN @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cS @ cN @ cS @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cS @ cN @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cN @ cS @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ A ) ) )
& ! [A: a,B: a,C: b] :
( ( cP @ cS @ A @ cS @ B @ C )
=> ( cP @ cN @ A @ cN @ B @ ( cG @ C ) ) )
& ! [A: a,B: a,C: b] :
( ( cP @ cN @ A @ cN @ B @ C )
=> ( cP @ cS @ A @ cS @ B @ ( cG @ C ) ) )
& ! [A: b] :
( ( cP @ cS @ cN @ cS @ cS @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cS @ cN @ cN @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cD @ A ) ) ) )
=> ? [A: b] : ( cP @ cN @ cN @ cN @ cN @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [A: b] :
( ( cP @ cS @ cN @ cS @ cN @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cS @ cN @ cS @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cS @ cN @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cN @ cS @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ A ) ) )
& ! [A: a,B: a,C: b] :
( ( cP @ cS @ A @ cS @ B @ C )
=> ( cP @ cN @ A @ cN @ B @ ( cG @ C ) ) )
& ! [A: a,B: a,C: b] :
( ( cP @ cN @ A @ cN @ B @ C )
=> ( cP @ cS @ A @ cS @ B @ ( cG @ C ) ) )
& ! [A: b] :
( ( cP @ cS @ cN @ cS @ cS @ A )
=> ( cP @ cN @ cN @ cS @ cN @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cN @ cS @ cN @ A )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cS @ cS @ cN @ cS @ A )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ A ) ) )
& ! [A: b] :
( ( cP @ cN @ cS @ cN @ cN @ A )
=> ( cP @ cS @ cS @ cN @ cS @ ( cD @ A ) ) ) )
=> ? [A: b] : ( cP @ cN @ cN @ cN @ cN @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ047^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.21 % Computer : n011.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 13:21:46 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.99 % [INFO] Parsing done (200ms).
% 1.23/1.01 % [INFO] Running in sequential loop mode.
% 2.14/1.42 % [INFO] eprover registered as external prover.
% 2.14/1.42 % [INFO] Scanning for conjecture ...
% 2.33/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.56/1.63 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.56/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.56/1.64 % [INFO] Type checking passed.
% 2.56/1.64 % [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 ...
% 4.04/2.27 % External prover 'e' found a proof!
% 4.04/2.27 % [INFO] Killing All external provers ...
% 4.04/2.27 % Time passed: 1916ms (effective reasoning time: 1258ms)
% 4.04/2.27 % 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)>
% 4.04/2.27 % Axioms used in derivation (0):
% 4.04/2.27 % No. of inferences in proof: 4
% 4.04/2.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1916 ms resp. 1258 ms w/o parsing
% 4.31/2.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.31/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------