%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM709^1 : 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 : n002.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 08:18:02 AM UTC 2026
% Result : Theorem 2.47s 1.22s
% Output : Refutation 2.47s
% 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 : 68 ( 4 ~; 0 |; 0 &; 64 @)
% ( 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 : 7 ( 5 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(pl_decl,type,
pl: nat > nat > nat ).
thf(ts_decl,type,
ts: nat > nat > nat ).
thf(suc_decl,type,
suc: nat > nat ).
thf(1,conjecture,
( ( pl @ ( ts @ x @ y ) @ y )
= ( ts @ ( suc @ x ) @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz28h) ).
thf(2,negated_conjecture,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( ts @ ( suc @ x ) @ y )
!= ( pl @ ( ts @ x @ y ) @ y ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ( ts @ ( suc @ A ) @ B )
= ( pl @ ( ts @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz28d) ).
thf(6,plain,
! [A: nat,B: nat] :
( ( ts @ ( suc @ A ) @ B )
= ( pl @ ( ts @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,plain,
! [B: nat,A: nat] :
( ( ts @ ( suc @ A ) @ B )
= ( pl @ ( ts @ A @ B ) @ B ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
! [B: nat,A: nat] :
( ( ts @ ( suc @ A ) @ B )
= ( pl @ ( ts @ A @ B ) @ B ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(9,plain,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( pl @ ( ts @ x @ y ) @ y ) ),
inference(rewrite,[status(thm)],[5,8]) ).
thf(10,plain,
$false,
inference(simp,[status(thm)],[9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM709^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n002.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 12:45:52 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
% 0.65/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.87/0.59 % [INFO] Parsing done (89ms).
% 0.87/0.60 % [INFO] Running in sequential loop mode.
% 1.15/0.79 % [INFO] eprover registered as external prover.
% 1.15/0.79 % [INFO] Scanning for conjecture ...
% 1.37/0.83 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.37/0.84 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.37/0.85 % [INFO] Problem is higher-order (TPTP THF).
% 1.37/0.85 % [INFO] Type checking passed.
% 1.37/0.86 % [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 ...
% 2.47/1.21 % [INFO] Killing All external provers ...
% 2.47/1.22 % Time passed: 917ms (effective reasoning time: 610ms)
% 2.47/1.22 % 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)>
% 2.47/1.22 % Axioms used in derivation (1): satz28d
% 2.47/1.22 % No. of inferences in proof: 10
% 2.47/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 917 ms resp. 610 ms w/o parsing
% 2.47/1.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.47/1.25 % [INFO] Killing All external provers ...
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