%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM668^1 : 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 08:17:56 AM UTC 2026
% Result : Theorem 1.97s 1.12s
% Output : Refutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 7 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 40 ( 12 ~; 0 |; 0 &; 28 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(1,conjecture,
~ ! [A: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz18) ).
thf(2,negated_conjecture,
~ ~ ! [A: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ! [A: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ A ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
~ ? [A: nat] :
( ( pl @ x @ y )
= ( pl @ x @ A ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(6,plain,
! [A: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
! [A: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
$false,
inference(pattern_uni,[status(thm)],[7:[bind(A,$thf( y ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM668^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % 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
% 0.09/0.21 % Computer : n007.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 12:31:40 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.63/0.52 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.86/0.61 % [INFO] Parsing done (91ms).
% 0.86/0.62 % [INFO] Running in sequential loop mode.
% 1.33/0.81 % [INFO] eprover registered as external prover.
% 1.33/0.81 % [INFO] Scanning for conjecture ...
% 1.33/0.86 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.33/0.87 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.33/0.87 % [INFO] Problem is higher-order (TPTP THF).
% 1.33/0.88 % [INFO] Type checking passed.
% 1.33/0.88 % [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 ...
% 1.97/1.12 % [INFO] Killing All external provers ...
% 1.97/1.12 % Time passed: 814ms (effective reasoning time: 497ms)
% 1.97/1.12 % 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)>
% 1.97/1.12 % Axioms used in derivation (0):
% 1.97/1.12 % No. of inferences in proof: 8
% 1.97/1.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 814 ms resp. 497 ms w/o parsing
% 2.38/1.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.38/1.14 % [INFO] Killing All external provers ...
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