%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP010+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : n009.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 : Sun Sep 27 07:35:31 AM UTC 2026
% Result : Theorem 4.41s 2.62s
% Output : Refutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 64 ( 6 ~; 0 |; 0 &; 48 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(ne_decl,type,
ne: $i > $o ).
thf(mem_decl,type,
mem: $i > $i > $o ).
thf(arr_decl,type,
arr: $i > $i > $i ).
thf(bool_decl,type,
bool: $i ).
thf(p_decl,type,
p: $i > $o ).
thf(ap_decl,type,
ap: $i > $i > $i ).
thf(c_2Ecardinal_2Ecardleq_decl,type,
c_2Ecardinal_2Ecardleq: $i > $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( B @ ne )
=> ! [C: $i] :
( ( bool @ ( A @ arr ) @ ( C @ mem ) )
=> ! [D: $i] :
( ( bool @ ( B @ arr ) @ ( D @ mem ) )
=> ( ~ ( D @ ( C @ ( B @ ( A @ c_2Ecardinal_2Ecardleq ) @ ap ) @ ap ) @ p )
<=> ~ ( D @ ( C @ ( B @ ( A @ c_2Ecardinal_2Ecardleq ) @ ap ) @ ap ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( B @ ne )
=> ! [C: $i] :
( ( bool @ ( A @ arr ) @ ( C @ mem ) )
=> ! [D: $i] :
( ( bool @ ( B @ arr ) @ ( D @ mem ) )
=> ( ~ ( D @ ( C @ ( B @ ( A @ c_2Ecardinal_2Ecardleq ) @ ap ) @ ap ) @ p )
<=> ~ ( D @ ( C @ ( B @ ( A @ c_2Ecardinal_2Ecardleq ) @ ap ) @ ap ) @ p ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,plain,
$false,
inference(simp,[status(thm)],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.13/0.40 % Computer : n009.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 17:12:44 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.22 % [INFO] Parsing done (238ms).
% 1.38/1.24 % [INFO] Running in sequential loop mode.
% 2.12/1.63 % [INFO] eprover registered as external prover.
% 2.12/1.64 % [INFO] Scanning for conjecture ...
% 2.34/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ...
% 2.52/1.86 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 2.74/1.94 % [INFO] Problem is first-order (TPTP FOF).
% 2.74/1.95 % [INFO] Type checking passed.
% 2.74/1.95 % [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 ...
% 4.41/2.62 % [INFO] Killing All external provers ...
% 4.41/2.62 % Time passed: 2082ms (effective reasoning time: 1373ms)
% 4.41/2.62 % 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)>
% 4.41/2.62 % Axioms used in derivation (0):
% 4.41/2.62 % No. of inferences in proof: 4
% 4.41/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2082 ms resp. 1373 ms w/o parsing
% 4.41/2.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.41/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------