%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM686^1 : 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 : n001.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 3.12s 2.08s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 2 ~; 0 |; 0 &; 79 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 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(u_decl,type,
u: nat ).
thf(some_decl,type,
some: ( nat > $o ) > $o ).
thf(diffprop_decl,type,
diffprop: nat > nat > nat > $o ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(4,axiom,
some @ ( diffprop @ z @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(10,plain,
some @ ( diffprop @ z @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ A @ B ) )
=> ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
thf(14,plain,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ A @ B ) )
=> ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
some @ ( diffprop @ x @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(9,plain,
some @ ( diffprop @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(17,plain,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(11,plain,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).
thf(2,negated_conjecture,
~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[10,14,9,17,11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM686^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.11/0.21 % Computer : n001.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 12:43:50 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
% 0.99/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.01 % [INFO] Parsing done (193ms).
% 1.15/1.02 % [INFO] Running in sequential loop mode.
% 1.92/1.41 % [INFO] eprover registered as external prover.
% 1.92/1.42 % [INFO] Scanning for conjecture ...
% 2.09/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.09/1.54 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.09/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.57 % [INFO] Type checking passed.
% 2.09/1.57 % [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 ...
% 3.12/2.07 % External prover 'e' found a proof!
% 3.12/2.07 % [INFO] Killing All external provers ...
% 3.12/2.07 % Time passed: 1693ms (effective reasoning time: 1046ms)
% 3.12/2.08 % 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)>
% 3.12/2.08 % Axioms used in derivation (5): n, m, satz15, satz19a, satz6
% 3.12/2.08 % No. of inferences in proof: 14
% 3.12/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1693 ms resp. 1046 ms w/o parsing
% 3.12/2.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.12/2.12 % [INFO] Killing All external provers ...
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