%------------------------------------------------------------------------------
% 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 : n001.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 08:06:19 AM UTC 2026
% Result : Theorem 4.09s 2.30s
% Output : Refutation 4.09s
% 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 : 12 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 54 ( 6 ~; 0 |; 0 &; 44 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(del_type,type,
del: $tType ).
thf(bool_decl,type,
bool: del ).
thf(arr_decl,type,
arr: del > del > del ).
thf(mem_decl,type,
mem: $i > del > $o ).
thf(ap_decl,type,
ap: $i > $i > $i ).
thf(p_decl,type,
p: $i > $o ).
thf(c_2Ecardinal_2Ecardleq_decl,type,
c_2Ecardinal_2Ecardleq: del > del > $i ).
thf(1,conjecture,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ B @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A @ B ) @ C ) @ D ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A @ B ) @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
thf(2,negated_conjecture,
~ ! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ B @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A @ B ) @ C ) @ D ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A @ B ) @ C ) @ D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(42,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,plain,
$false,
inference(simp,[status(thm)],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % 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
% 0.11/0.20 % Computer : n001.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 19:31:36 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.02/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.52/1.06 % [INFO] Parsing done (247ms).
% 1.52/1.07 % [INFO] Running in sequential loop mode.
% 2.22/1.46 % [INFO] eprover registered as external prover.
% 2.22/1.47 % [INFO] Scanning for conjecture ...
% 2.41/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 39 axioms. Running axiom selection ...
% 2.58/1.68 % [INFO] Axiom selection finished. Selected 39 axioms (removed 0 axioms).
% 2.79/1.76 % [INFO] Problem is higher-order (TPTP THF).
% 2.79/1.77 % [INFO] Type checking passed.
% 2.79/1.78 % [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 ...
% 3.84/2.30 % [INFO] Killing All external provers ...
% 4.09/2.30 % Time passed: 1940ms (effective reasoning time: 1219ms)
% 4.09/2.30 % 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)>
% 4.09/2.30 % Axioms used in derivation (0):
% 4.09/2.30 % No. of inferences in proof: 4
% 4.09/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1940 ms resp. 1219 ms w/o parsing
% 4.09/2.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.09/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------