%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM666^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n012.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 08:17:55 AM UTC 2026
% Result : Theorem 1.71s 1.01s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 2 ~; 0 |; 0 &; 43 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(z_decl,type,
z: nat ).
thf(some_decl,type,
some: ( nat > $o ) > $o ).
thf(diffprop_decl,type,
diffprop: nat > nat > nat > $o ).
thf(moreis_decl,type,
moreis: nat > nat > $o ).
thf(lessis_decl,type,
lessis: nat > nat > $o ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( lessis @ A @ B )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a) ).
thf(10,plain,
! [A: nat,B: nat,C: nat] :
( ( lessis @ A @ B )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
moreis @ y @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(9,plain,
moreis @ y @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( moreis @ A @ B )
=> ( lessis @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz13) ).
thf(13,plain,
! [A: nat,B: nat] :
( ( moreis @ A @ B )
=> ( lessis @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
some @ ( diffprop @ x @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16d) ).
thf(2,negated_conjecture,
~ ( some @ ( diffprop @ x @ z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( some @ ( diffprop @ x @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
some @ ( diffprop @ x @ y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(8,plain,
some @ ( diffprop @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,plain,
$false,
inference(e,[status(thm)],[10,9,13,7,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM666^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % 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
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Tue Sep 29 12:33:48 UTC 2026
% 0.06/0.13 % CPUTime :
% 0.06/0.13 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
% 0.41/0.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.57/0.51 % [INFO] Parsing done (90ms).
% 0.57/0.51 % [INFO] Running in sequential loop mode.
% 1.00/0.70 % [INFO] eprover registered as external prover.
% 1.00/0.70 % [INFO] Scanning for conjecture ...
% 1.00/0.74 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.00/0.76 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.00/0.77 % [INFO] Problem is higher-order (TPTP THF).
% 1.00/0.77 % [INFO] Type checking passed.
% 1.00/0.77 % [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 ...
% 1.39/1.01 % External prover 'e' found a proof!
% 1.39/1.01 % [INFO] Killing All external provers ...
% 1.71/1.01 % Time passed: 808ms (effective reasoning time: 494ms)
% 1.71/1.01 % 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)>
% 1.71/1.01 % Axioms used in derivation (4): satz16a, n, satz13, m
% 1.71/1.01 % No. of inferences in proof: 12
% 1.71/1.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 808 ms resp. 494 ms w/o parsing
% 1.71/1.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.71/1.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------