%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM640^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n020.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 08:17:51 AM UTC 2026
% Result : Theorem 2.49s 1.20s
% Output : Refutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 58 ( 4 ~; 0 |; 0 &; 54 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(suc_decl,type,
suc: nat > nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(1,conjecture,
( ( suc @ ( pl @ x @ y ) )
= ( pl @ x @ ( suc @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4f) ).
thf(2,negated_conjecture,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ x @ ( suc @ y ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ x @ ( suc @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( pl @ x @ ( suc @ y ) )
!= ( suc @ ( pl @ x @ y ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ( pl @ A @ ( suc @ B ) )
= ( suc @ ( pl @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4b) ).
thf(6,plain,
! [A: nat,B: nat] :
( ( pl @ A @ ( suc @ B ) )
= ( suc @ ( pl @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,plain,
! [B: nat,A: nat] :
( ( pl @ A @ ( suc @ B ) )
= ( suc @ ( pl @ A @ B ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
! [B: nat,A: nat] :
( ( pl @ A @ ( suc @ B ) )
= ( suc @ ( pl @ A @ B ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(9,plain,
( ( suc @ ( pl @ x @ y ) )
!= ( suc @ ( pl @ x @ y ) ) ),
inference(rewrite,[status(thm)],[5,8]) ).
thf(10,plain,
$false,
inference(simp,[status(thm)],[9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM640^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.11/0.22 % Computer : n020.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 12:15:04 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.63/0.56 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.96/0.65 % [INFO] Parsing done (94ms).
% 0.96/0.67 % [INFO] Running in sequential loop mode.
% 1.29/0.86 % [INFO] eprover registered as external prover.
% 1.29/0.87 % [INFO] Scanning for conjecture ...
% 1.53/0.90 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.53/0.92 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.53/0.93 % [INFO] Problem is higher-order (TPTP THF).
% 1.53/0.93 % [INFO] Type checking passed.
% 1.53/0.93 % [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 ...
% 2.49/1.20 % [INFO] Killing All external provers ...
% 2.49/1.20 % Time passed: 851ms (effective reasoning time: 527ms)
% 2.49/1.20 % 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)>
% 2.49/1.20 % Axioms used in derivation (1): satz4b
% 2.49/1.20 % No. of inferences in proof: 10
% 2.49/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 851 ms resp. 527 ms w/o parsing
% 2.49/1.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.49/1.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------