%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP010^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : n014.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 5.87s 2.77s
% Output : Refutation 6.17s
% 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 : 8 ( 2 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 58 ( 6 ~; 0 |; 0 &; 52 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(u_type,type,
u: $tType ).
thf(d_type,type,
d: $tType ).
thf(du_type,type,
du: $tType ).
thf(tyop_2Emin_2Ebool_decl,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun_decl,type,
tyop_2Emin_2Efun: d > d > d ).
thf(s_decl,type,
s: d > u > du ).
thf(c_2Ecardinal_2Ecardleq_2E2_decl,type,
c_2Ecardinal_2Ecardleq_2E2: du > du > u ).
thf(j_mono_2Etyop_2Emin_2Ebool_decl,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(1,conjecture,
! [A: d,B: d,C: u,D: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
thf(2,negated_conjecture,
~ ! [A: d,B: d,C: u,D: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(34,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,plain,
$false,
inference(simp,[status(thm)],[34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.11/0.23 % Computer : n014.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 19:24:59 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 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
% 1.09/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.63/1.09 % [INFO] Parsing done (277ms).
% 1.63/1.11 % [INFO] Running in sequential loop mode.
% 2.77/1.51 % [INFO] eprover registered as external prover.
% 2.77/1.52 % [INFO] Scanning for conjecture ...
% 2.96/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 41 axioms. Running axiom selection ...
% 3.18/1.74 % [INFO] Axiom selection finished. Selected 31 axioms (removed 10 axioms).
% 3.44/1.84 % [INFO] Problem is higher-order (TPTP THF).
% 3.44/1.85 % [INFO] Type checking passed.
% 3.44/1.86 % [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 ...
% 5.87/2.77 % [INFO] Killing All external provers ...
% 5.87/2.77 % Time passed: 2392ms (effective reasoning time: 1654ms)
% 5.87/2.77 % 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)>
% 5.87/2.77 % Axioms used in derivation (0):
% 5.87/2.77 % No. of inferences in proof: 4
% 5.87/2.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2392 ms resp. 1654 ms w/o parsing
% 6.17/2.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.17/2.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------