%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU905^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:29:34 AM UTC 2026
% Result : Theorem 4.49s 2.44s
% Output : Refutation 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 9 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 314 ( 8 ~; 0 |; 57 &; 210 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 19 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% Number of variables : 87 ( 0 ^; 87 !; 0 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(1,conjecture,
! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
( ~ ( ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( C @ ( D @ I @ J ) ) )
& ! [I: a,J: a] :
( ( ( G @ I )
& ( G @ J ) )
=> ( G @ ( H @ I @ J ) ) )
& ! [I: g] :
( ( C @ I )
=> ( G @ ( B @ ( A @ I ) ) ) )
& ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( ( B @ ( A @ ( D @ I @ J ) ) )
= ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) )
=> ~ ( ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( C @ ( D @ I @ J ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( E @ ( F @ I @ J ) ) )
& ! [I: g] :
( ( C @ I )
=> ( E @ ( A @ I ) ) )
& ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( ( A @ ( D @ I @ J ) )
= ( F @ ( A @ I ) @ ( A @ J ) ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( E @ ( F @ I @ J ) ) )
& ! [I: a,J: a] :
( ( ( G @ I )
& ( G @ J ) )
=> ( G @ ( H @ I @ J ) ) )
& ! [I: b] :
( ( E @ I )
=> ( G @ ( B @ I ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( ( B @ ( F @ I @ J ) )
= ( H @ ( B @ I ) @ ( B @ J ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM126A_pme) ).
thf(2,negated_conjecture,
~ ! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
( ~ ( ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( C @ ( D @ I @ J ) ) )
& ! [I: a,J: a] :
( ( ( G @ I )
& ( G @ J ) )
=> ( G @ ( H @ I @ J ) ) )
& ! [I: g] :
( ( C @ I )
=> ( G @ ( B @ ( A @ I ) ) ) )
& ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( ( B @ ( A @ ( D @ I @ J ) ) )
= ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) )
=> ~ ( ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( C @ ( D @ I @ J ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( E @ ( F @ I @ J ) ) )
& ! [I: g] :
( ( C @ I )
=> ( E @ ( A @ I ) ) )
& ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( ( A @ ( D @ I @ J ) )
= ( F @ ( A @ I ) @ ( A @ J ) ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( E @ ( F @ I @ J ) ) )
& ! [I: a,J: a] :
( ( ( G @ I )
& ( G @ J ) )
=> ( G @ ( H @ I @ J ) ) )
& ! [I: b] :
( ( E @ I )
=> ( G @ ( B @ I ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( ( B @ ( F @ I @ J ) )
= ( H @ ( B @ I ) @ ( B @ J ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
( ~ ( ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( C @ ( D @ I @ J ) ) )
& ! [I: a,J: a] :
( ( ( G @ I )
& ( G @ J ) )
=> ( G @ ( H @ I @ J ) ) )
& ! [I: g] :
( ( C @ I )
=> ( G @ ( B @ ( A @ I ) ) ) )
& ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( ( B @ ( A @ ( D @ I @ J ) ) )
= ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) )
=> ~ ( ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( C @ ( D @ I @ J ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( E @ ( F @ I @ J ) ) )
& ! [I: g] :
( ( C @ I )
=> ( E @ ( A @ I ) ) )
& ! [I: g,J: g] :
( ( ( C @ I )
& ( C @ J ) )
=> ( ( A @ ( D @ I @ J ) )
= ( F @ ( A @ I ) @ ( A @ J ) ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( E @ ( F @ I @ J ) ) )
& ! [I: a,J: a] :
( ( ( G @ I )
& ( G @ J ) )
=> ( G @ ( H @ I @ J ) ) )
& ! [I: b] :
( ( E @ I )
=> ( G @ ( B @ I ) ) )
& ! [I: b,J: b] :
( ( ( E @ I )
& ( E @ J ) )
=> ( ( B @ ( F @ I @ J ) )
= ( H @ ( B @ I ) @ ( B @ J ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU905^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.22 % Computer : n001.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 14:50:50 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (197ms).
% 1.24/1.02 % [INFO] Running in sequential loop mode.
% 2.19/1.41 % [INFO] eprover registered as external prover.
% 2.19/1.42 % [INFO] Scanning for conjecture ...
% 2.40/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.57/1.60 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.57/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.57/1.61 % [INFO] Type checking passed.
% 2.57/1.61 % [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 ...
% 4.49/2.43 % External prover 'e' found a proof!
% 4.49/2.43 % [INFO] Killing All external provers ...
% 4.49/2.44 % Time passed: 2068ms (effective reasoning time: 1413ms)
% 4.49/2.44 % 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)>
% 4.49/2.44 % Axioms used in derivation (0):
% 4.49/2.44 % No. of inferences in proof: 4
% 4.49/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2068 ms resp. 1413 ms w/o parsing
% 4.49/2.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.49/2.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------