%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV232^5 : 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 : n019.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 08:37:02 AM UTC 2026
% Result : Theorem 2.23s 1.64s
% Output : Refutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 2 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 34 ( 2 ~; 0 |; 4 &; 20 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 4 ^; 8 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(cS_decl,type,
cS: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(c0_decl,type,
c0: ( $i > $o ) > $o ).
thf(1,conjecture,
( ( ^ [A: ( $i > $o ) > $o] :
! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ c0 )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B @ ( cS @ C ) ) ) )
=> ( B @ A ) ) )
= ( ^ [A: ( $i > $o ) > $o] :
! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ c0 )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B @ ( cS @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6007_pme) ).
thf(2,negated_conjecture,
( ( ^ [A: ( $i > $o ) > $o] :
! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ c0 )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B @ ( cS @ C ) ) ) )
=> ( B @ A ) ) )
!= ( ^ [A: ( $i > $o ) > $o] :
! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ c0 )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B @ ( cS @ C ) ) ) )
=> ( B @ A ) ) ) ),
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 : SEV232^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.12/0.20 % Computer : n019.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.21 % DateTime : Tue Sep 29 15:23:32 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 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
% 0.84/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.94 % [INFO] Parsing done (179ms).
% 1.16/0.96 % [INFO] Running in sequential loop mode.
% 1.72/1.35 % [INFO] eprover registered as external prover.
% 1.72/1.36 % [INFO] Scanning for conjecture ...
% 1.90/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.90/1.47 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.90/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.48 % [INFO] Type checking passed.
% 1.90/1.48 % [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 ...
% 2.23/1.63 % [INFO] Killing All external provers ...
% 2.23/1.63 % Time passed: 1291ms (effective reasoning time: 668ms)
% 2.23/1.63 % 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)>
% 2.23/1.64 % Axioms used in derivation (0):
% 2.23/1.64 % No. of inferences in proof: 4
% 2.23/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1291 ms resp. 668 ms w/o parsing
% 2.23/1.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.23/1.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------