%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM638^1 : 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 : n007.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 3.00s 1.84s
% Output : Refutation 3.00s
% 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 : 28 ( 22 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 45 ( 12 ~; 0 |; 0 &; 20 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 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 : 17 ( 5 ^; 12 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(n_1_decl,type,
n_1: nat ).
thf(suc_decl,type,
suc: nat > nat ).
thf(some_decl,type,
some: ( nat > $o ) > $o ).
thf(1,conjecture,
~ ( ! [A: nat,B: nat] :
( ( x
= ( suc @ A ) )
=> ( ( x
= ( suc @ B ) )
=> ( A = B ) ) )
=> ~ ( some
@ ^ [A: nat] :
( x
= ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3a) ).
thf(2,negated_conjecture,
~ ~ ( ! [A: nat,B: nat] :
( ( x
= ( suc @ A ) )
=> ( ( x
= ( suc @ B ) )
=> ( A = B ) ) )
=> ~ ( some
@ ^ [A: nat] :
( x
= ( suc @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ~ ( ! [A: nat,B: nat] :
( ( x
= ( suc @ A ) )
=> ( ( x
= ( suc @ B ) )
=> ( A = B ) ) )
=> ~ ( some
@ ^ [A: nat] :
( x
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
x != n_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(16,plain,
x != n_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(19,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: nat] :
( ( A != n_1 )
=> ( some
@ ^ [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3) ).
thf(24,plain,
! [A: nat] :
( ( A != n_1 )
=> ( some
@ ^ [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,plain,
$false,
inference(e,[status(thm)],[6,16,19,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM638^1 : 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
% 0.11/0.22 % Computer : n007.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 12:10:55 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.99/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (172ms).
% 1.17/0.99 % [INFO] Running in sequential loop mode.
% 1.77/1.39 % [INFO] eprover registered as external prover.
% 1.77/1.39 % [INFO] Scanning for conjecture ...
% 1.96/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.96/1.46 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.96/1.47 % [INFO] Problem is higher-order (TPTP THF).
% 1.96/1.47 % [INFO] Type checking passed.
% 1.96/1.47 % [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 ...
% 3.00/1.84 % External prover 'e' found a proof!
% 3.00/1.84 % [INFO] Killing All external provers ...
% 3.00/1.84 % Time passed: 1473ms (effective reasoning time: 839ms)
% 3.00/1.84 % 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)>
% 3.00/1.84 % Axioms used in derivation (3): n, ax4, satz3
% 3.00/1.84 % No. of inferences in proof: 10
% 3.00/1.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1473 ms resp. 839 ms w/o parsing
% 3.00/1.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.00/1.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------