%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM684^1 : 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 : n019.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 08:17:58 AM UTC 2026
% Result : Theorem 3.37s 2.08s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 2 ~; 0 |; 0 &; 24 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(z_decl,type,
z: nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(1,conjecture,
x = y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz20e) ).
thf(2,negated_conjecture,
x != y,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
x != y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
( ( pl @ z @ x )
= ( pl @ z @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i) ).
thf(8,plain,
( ( pl @ z @ x )
= ( pl @ z @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( pl @ A @ C )
= ( pl @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz20b) ).
thf(10,plain,
! [A: nat,B: nat,C: nat] :
( ( ( pl @ A @ C )
= ( pl @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(16,plain,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[6,8,10,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM684^1 : 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 : n019.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 12:37:18 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
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (185ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.02/1.41 % [INFO] eprover registered as external prover.
% 2.02/1.42 % [INFO] Scanning for conjecture ...
% 2.02/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.21/1.52 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.21/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.55 % [INFO] Type checking passed.
% 2.21/1.55 % [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 ...
% 3.37/2.07 % External prover 'e' found a proof!
% 3.37/2.07 % [INFO] Killing All external provers ...
% 3.37/2.08 % Time passed: 1724ms (effective reasoning time: 1068ms)
% 3.37/2.08 % 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)>
% 3.37/2.08 % Axioms used in derivation (3): i, satz20b, satz6
% 3.37/2.08 % No. of inferences in proof: 10
% 3.37/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1724 ms resp. 1068 ms w/o parsing
% 3.37/2.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.37/2.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------