%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM695_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : n026.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 08:09:40 AM UTC 2026
% Result : Theorem 3.84s 2.41s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 11 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 67 ( 10 ~; 2 |; 0 &; 55 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 ^; 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(more_decl,type,
more: nat > nat > $o ).
thf(suc_decl,type,
suc: nat > nat ).
thf(n_1_decl,type,
n_1: nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(6,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ pl ) @ more ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz18) ).
thf(18,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ pl ) @ more ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [B: nat,A: nat] : ( A @ ( B @ ( A @ pl ) @ more ) ),
inference(cnf,[status(esa)],[18]) ).
thf(1,conjecture,
n_1 @ ( x @ suc @ more ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24b) ).
thf(2,negated_conjecture,
~ ( n_1 @ ( x @ suc @ more ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( n_1 @ ( x @ suc @ more ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
! [B: nat,A: nat] :
( ( ( A @ ( B @ ( A @ pl ) @ more ) )
!= ( n_1 @ ( x @ suc @ more ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,8]) ).
thf(26,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ ( A @ pl ) @ more ) )
!= ( n_1 @ ( x @ suc @ more ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
! [B: nat,A: nat] :
( ( A != n_1 )
| ( ( B @ ( A @ pl ) )
!= ( x @ suc ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
! [A: nat] :
( ( A @ ( n_1 @ pl ) )
!= ( x @ suc ) ),
inference(simp,[status(thm)],[27]) ).
thf(7,axiom,
! [A: nat] :
( ( A @ suc )
= ( A @ ( n_1 @ pl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4g) ).
thf(20,plain,
! [A: nat] :
( ( A @ suc )
= ( A @ ( n_1 @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,plain,
! [A: nat] :
( ( A @ suc )
= ( A @ ( n_1 @ pl ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [A: nat] :
( ( A @ ( n_1 @ pl ) )
= ( A @ suc ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(29,plain,
! [A: nat] :
( ( A @ suc )
!= ( x @ suc ) ),
inference(rewrite,[status(thm)],[28,22]) ).
thf(30,plain,
! [A: nat] : ( A != x ),
inference(simp,[status(thm)],[29]) ).
thf(32,plain,
$false,
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( x ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM695_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.14/0.40 % Computer : n026.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 03:50:25 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.89/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.16 % [INFO] Parsing done (186ms).
% 1.28/1.18 % [INFO] Running in sequential loop mode.
% 1.82/1.58 % [INFO] eprover registered as external prover.
% 1.82/1.59 % [INFO] Scanning for conjecture ...
% 2.02/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.21/1.71 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.21/1.74 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.21/1.74 % [INFO] Type checking passed.
% 2.21/1.75 % [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 ...
% 3.84/2.41 % [INFO] Killing All external provers ...
% 3.84/2.41 % Time passed: 1868ms (effective reasoning time: 1224ms)
% 3.84/2.41 % 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)>
% 3.84/2.41 % Axioms used in derivation (2): satz18, satz4g
% 3.84/2.41 % No. of inferences in proof: 17
% 3.84/2.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1868 ms resp. 1224 ms w/o parsing
% 3.84/2.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.84/2.45 % [INFO] Killing All external provers ...
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