%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN986+1.000 : TPTP v9.3.1. Released v4.0.0.
% 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 : n005.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 : Sun Sep 27 09:20:33 AM UTC 2026
% Result : Theorem 3.15s 2.26s
% Output : Refutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 2 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 6 ~; 1 |; 0 &; 38 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-3 aty)
% Number of variables : 11 ( 0 ^; 8 !; 3 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(r_decl,type,
r: $i > $i > $i > $o ).
thf(zero_decl,type,
zero: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(3,axiom,
! [A: $i] : ( A @ succ @ ( zero @ ( A @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hyp1) ).
thf(7,plain,
! [A: $i] : ( A @ succ @ ( zero @ ( A @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [A: $i] : ( A @ succ @ ( zero @ ( A @ r ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(1,conjecture,
? [A: $i] : ( A @ ( zero @ ( zero @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ck) ).
thf(2,negated_conjecture,
~ ? [A: $i] : ( A @ ( zero @ ( zero @ r ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ? [A: $i] : ( A @ ( zero @ ( zero @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [A: $i] :
~ ( A @ ( zero @ ( zero @ r ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( ( A @ succ @ ( zero @ ( A @ r ) ) )
!= ( B @ ( zero @ ( zero @ r ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,6]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( A @ succ @ ( zero @ ( A @ r ) ) )
!= ( B @ ( zero @ ( zero @ r ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
$false,
inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( zero )),bind(B,$thf( zero @ succ ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.000 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.12/0.40 % Computer : n005.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sat Sep 26 18:53:17 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 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
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.17 % [INFO] Parsing done (180ms).
% 1.17/1.18 % [INFO] Running in sequential loop mode.
% 1.80/1.59 % [INFO] eprover registered as external prover.
% 1.98/1.60 % [INFO] Scanning for conjecture ...
% 1.98/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.14/1.71 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.14/1.73 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.73 % [INFO] Type checking passed.
% 2.14/1.74 % [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 ...
% 3.15/2.26 % [INFO] Killing All external provers ...
% 3.15/2.26 % Time passed: 1706ms (effective reasoning time: 1069ms)
% 3.15/2.26 % 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)>
% 3.15/2.26 % Axioms used in derivation (1): hyp1
% 3.15/2.26 % No. of inferences in proof: 10
% 3.15/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1706 ms resp. 1069 ms w/o parsing
% 3.15/2.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/2.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------