%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM635^2 : 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 : n015.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 08:17:50 AM UTC 2026
% Result : Theorem 4.74s 2.50s
% Output : Refutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 43 ( 10 ~; 0 |; 2 &; 22 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(one_decl,type,
one: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( succ @ A )
!= ( succ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( A != B )
=> ( ( succ @ A )
!= ( succ @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i,B: $i] :
( ( A != B )
=> ( ( succ @ A )
!= ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( succ @ A )
!= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_is_first) ).
thf(12,plain,
! [A: $i] :
( ( succ @ A )
!= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( succ @ A )
= ( succ @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_injective) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( ( succ @ A )
= ( succ @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i > $o] :
( ( ( A @ one )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( succ @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(21,plain,
! [A: $i > $o] :
( ( ( A @ one )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( succ @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[6,12,16,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM635^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.11/0.21 % Computer : n015.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % 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 12:02:47 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.16/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.67/1.16 % [INFO] Parsing done (197ms).
% 1.67/1.18 % [INFO] Running in sequential loop mode.
% 2.41/1.61 % [INFO] eprover registered as external prover.
% 2.41/1.62 % [INFO] Scanning for conjecture ...
% 2.64/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.64/1.75 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.64/1.76 % [INFO] Problem is higher-order (TPTP THF).
% 2.64/1.76 % [INFO] Type checking passed.
% 2.64/1.77 % [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 ...
% 4.74/2.50 % External prover 'e' found a proof!
% 4.74/2.50 % [INFO] Killing All external provers ...
% 4.74/2.50 % Time passed: 2090ms (effective reasoning time: 1315ms)
% 4.74/2.50 % 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)>
% 4.74/2.50 % Axioms used in derivation (3): one_is_first, succ_injective, induction
% 4.74/2.50 % No. of inferences in proof: 10
% 4.74/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2090 ms resp. 1315 ms w/o parsing
% 4.74/2.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.74/2.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------