%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN986+1.003 : 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 : 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 : Sun Sep 27 09:20:34 AM UTC 2026
% Result : Theorem 5.15s 3.31s
% Output : Refutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 2 ~; 0 |; 9 &; 64 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 2 con; 0-3 aty)
% Number of variables : 22 ( 0 ^; 10 !; 12 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(r_decl,type,
r: $i > $i > $i > $o ).
thf(zero_decl,type,
zero: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(1,conjecture,
? [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( zero @ r ) ) )
& ( C @ ( B @ ( zero @ r ) ) )
& ( B @ ( A @ ( zero @ r ) ) )
& ( A @ ( zero @ ( zero @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ck) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( zero @ r ) ) )
& ( C @ ( B @ ( zero @ r ) ) )
& ( B @ ( A @ ( zero @ r ) ) )
& ( A @ ( zero @ ( zero @ r ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ? [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( zero @ r ) ) )
& ( C @ ( B @ ( zero @ r ) ) )
& ( B @ ( A @ ( zero @ r ) ) )
& ( A @ ( zero @ ( zero @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] : ( A @ succ @ ( zero @ ( A @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hyp1) ).
thf(8,plain,
! [A: $i] : ( A @ succ @ ( zero @ ( A @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ r ) ) )
=> ( ( D @ ( B @ ( C @ r ) ) )
=> ( D @ ( B @ succ @ ( A @ r ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hyp2) ).
thf(10,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ r ) ) )
=> ( ( D @ ( B @ ( C @ r ) ) )
=> ( D @ ( B @ succ @ ( A @ r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[5,8,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.22/0.48 % Computer : n020.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sat Sep 26 18:54:33 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.39/1.30 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.72/1.57 % [INFO] Parsing done (265ms).
% 1.72/1.59 % [INFO] Running in sequential loop mode.
% 2.81/2.17 % [INFO] eprover registered as external prover.
% 2.81/2.18 % [INFO] Scanning for conjecture ...
% 3.07/2.31 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 3.07/2.37 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 3.07/2.38 % [INFO] Problem is first-order (TPTP FOF).
% 3.07/2.39 % [INFO] Type checking passed.
% 3.07/2.40 % [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 ...
% 5.15/3.30 % External prover 'e' found a proof!
% 5.15/3.30 % [INFO] Killing All external provers ...
% 5.15/3.30 % Time passed: 2623ms (effective reasoning time: 1703ms)
% 5.15/3.30 % 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)>
% 5.15/3.30 % Axioms used in derivation (2): hyp1, hyp2
% 5.15/3.30 % No. of inferences in proof: 8
% 5.15/3.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2623 ms resp. 1703 ms w/o parsing
% 5.15/3.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.15/3.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------