%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM004-1 : TPTP v9.3.1. Released v1.1.0.
% 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 : n018.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 06:57:50 AM UTC 2026
% Result : Unsatisfiable 4.01s 7.22s
% Output : Refutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 104 ( 10 ~; 8 |; 0 &; 86 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(failure_node_decl,type,
failure_node: $i > $i > $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(empty_decl,type,
empty: $i ).
thf(parent_of_decl,type,
parent_of: $i > $i > $i ).
thf(contradictory_decl,type,
contradictory: $i > $i > $o ).
thf(siblings_decl,type,
siblings: $i > $i > $o ).
thf(negate_decl,type,
negate: $i > $i ).
thf(left_child_of_decl,type,
left_child_of: $i > $i ).
thf(right_child_of_decl,type,
right_child_of: $i > $i ).
thf(n_left_decl,type,
n_left: $i ).
thf(atom_decl,type,
atom: $i ).
thf(n_right_decl,type,
n_right: $i ).
thf(n_decl,type,
n: $i ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( empty @ ( empty @ or ) @ ( A @ failure_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_is_there_an_empty_node) ).
thf(10,plain,
! [A: $i] :
~ ( empty @ ( empty @ or ) @ ( A @ failure_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ negate @ contradictory ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_x_contradicts_x) ).
thf(14,plain,
! [A: $i] : ( A @ ( A @ negate @ contradictory ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
( n_right
= ( n @ right_child_of ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_right_equals_right_child_of_n) ).
thf(21,plain,
( n_right
= ( n @ right_child_of ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
atom @ ( empty @ or ) @ ( n_left @ failure_node ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_left_is_atom) ).
thf(17,plain,
atom @ ( empty @ or ) @ ( n_left @ failure_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ siblings ) )
| ~ ( F @ ( E @ contradictory ) )
| ~ ( F @ ( D @ or ) @ ( B @ failure_node ) )
| ~ ( E @ ( C @ or ) @ ( A @ failure_node ) )
| ( D @ ( C @ or ) @ ( B @ ( A @ parent_of ) @ failure_node ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',make_node) ).
thf(12,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ siblings ) )
| ~ ( F @ ( E @ contradictory ) )
| ~ ( F @ ( D @ or ) @ ( B @ failure_node ) )
| ~ ( E @ ( C @ or ) @ ( A @ failure_node ) )
| ( D @ ( C @ or ) @ ( B @ ( A @ parent_of ) @ failure_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
atom @ negate @ ( empty @ or ) @ ( n_right @ failure_node ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_right_is_not_atom) ).
thf(18,plain,
atom @ negate @ ( empty @ or ) @ ( n_right @ failure_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] : ( A @ right_child_of @ ( A @ left_child_of @ siblings ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_left_and_n_right_are_siblings) ).
thf(16,plain,
! [A: $i] : ( A @ right_child_of @ ( A @ left_child_of @ siblings ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
( n_left
= ( n @ left_child_of ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_left_equals_left_child_of_n) ).
thf(19,plain,
( n_left
= ( n @ left_child_of ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] : ( A @ negate @ ( A @ contradictory ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_contradicts_not_x) ).
thf(15,plain,
! [A: $i] : ( A @ negate @ ( A @ contradictory ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
$false,
inference(e,[status(thm)],[10,14,21,17,12,18,16,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM004-1 : TPTP v9.3.1. Released v1.1.0.
% 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
% 0.15/5.42 % Computer : n018.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Sat Sep 26 23:21:28 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.42 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
% 0.20/5.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/6.08 % [INFO] Parsing done (154ms).
% 1.36/6.09 % [INFO] Running in sequential loop mode.
% 1.82/6.42 % [INFO] eprover registered as external prover.
% 2.08/6.43 % [INFO] Scanning for conjecture ...
% 2.22/6.50 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.22/6.53 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.22/6.55 % [INFO] Problem is propositional (TPTP CNF).
% 2.22/6.55 % [INFO] Type checking passed.
% 2.22/6.56 % [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 ...
% 4.01/7.22 % External prover 'e' found a proof!
% 4.01/7.22 % [INFO] Killing All external provers ...
% 4.01/7.22 % Time passed: 1654ms (effective reasoning time: 1122ms)
% 4.01/7.22 % Axioms used in derivation (8): n_right_equals_right_child_of_n, x_contradicts_not_x, n_left_and_n_right_are_siblings, n_left_equals_left_child_of_n, n_right_is_not_atom, not_x_contradicts_x, make_node, n_left_is_atom
% 4.01/7.22 % No. of inferences in proof: 19
% 4.01/7.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1654 ms resp. 1122 ms w/o parsing
% 4.01/7.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.01/7.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------