%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM003_1 : TPTP v9.3.1. Released v5.0.0.
% 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 : n004.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 : Theorem 5.06s 3.07s
% Output : Refutation 5.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 0 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 260 ( 17 ~; 0 |; 28 &; 187 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 47 ( 0 ^; 32 !; 15 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(program_type,type,
program: $tType ).
thf(algorithm_type,type,
algorithm: $tType ).
thf(input_type,type,
input: $tType ).
thf(output_type,type,
output: $tType ).
thf(bad_decl,type,
bad: output ).
thf(good_decl,type,
good: output ).
thf(decides_decl,type,
decides: algorithm > program > input > $o ).
thf(halts2_decl,type,
halts2: program > input > $o ).
thf(halts3_decl,type,
halts3: program > program > input > $o ).
thf(outputs_decl,type,
outputs: program > output > $o ).
thf(algorithm_of_decl,type,
algorithm_of: program > algorithm ).
thf(as_input_decl,type,
as_input: program > input ).
thf(3,axiom,
( ? [A: algorithm] :
! [B: program,C: input] : ( C @ ( B @ ( A @ decides ) ) )
=> ? [A: program] :
! [B: program,C: input] : ( C @ ( B @ ( A @ algorithm_of @ decides ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(10,plain,
( ? [A: algorithm] :
! [B: program,C: input] : ( C @ ( B @ ( A @ decides ) ) )
=> ? [A: program] :
! [B: program,C: input] : ( C @ ( B @ ( A @ algorithm_of @ decides ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
( ? [A: program] :
! [B: program] :
( ( ~ ( B @ as_input @ ( B @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( B @ as_input @ ( B @ ( A @ halts3 ) ) ) ) )
& ( ( B @ as_input @ ( B @ halts2 ) )
=> ( ( good @ ( A @ outputs ) )
& ( B @ as_input @ ( B @ ( A @ halts3 ) ) ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ~ ( B @ as_input @ ( B @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) )
& ( ( B @ as_input @ ( B @ halts2 ) )
=> ( ( good @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(21,plain,
( ? [A: program] :
! [B: program] :
( ( ~ ( B @ as_input @ ( B @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( B @ as_input @ ( B @ ( A @ halts3 ) ) ) ) )
& ( ( B @ as_input @ ( B @ halts2 ) )
=> ( ( good @ ( A @ outputs ) )
& ( B @ as_input @ ( B @ ( A @ halts3 ) ) ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ~ ( B @ as_input @ ( B @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) )
& ( ( B @ as_input @ ( B @ halts2 ) )
=> ( ( good @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: program,B: program,C: input] :
( ( C @ ( B @ ( A @ algorithm_of @ decides ) ) )
=> ! [D: program,E: input] :
( ( ~ ( E @ ( D @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( E @ ( D @ ( A @ halts3 ) ) ) ) )
& ( ( E @ ( D @ halts2 ) )
=> ( ( good @ ( A @ outputs ) )
& ( E @ ( D @ ( A @ halts3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(12,plain,
! [A: program,B: program,C: input] :
( ( C @ ( B @ ( A @ algorithm_of @ decides ) ) )
=> ! [D: program,E: input] :
( ( ~ ( E @ ( D @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( E @ ( D @ ( A @ halts3 ) ) ) ) )
& ( ( E @ ( D @ halts2 ) )
=> ( ( good @ ( A @ outputs ) )
& ( E @ ( D @ ( A @ halts3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
~ ? [A: algorithm] :
! [B: program,C: input] : ( C @ ( B @ ( A @ decides ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
~ ~ ? [A: algorithm] :
! [B: program,C: input] : ( C @ ( B @ ( A @ decides ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ~ ? [A: algorithm] :
! [B: program,C: input] : ( C @ ( B @ ( A @ decides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
( ? [A: program] :
! [B: program] :
( ( ~ ( B @ as_input @ ( B @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) )
& ( ( B @ as_input @ ( B @ halts2 ) )
=> ( ( good @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ~ ( B @ as_input @ ( B @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) )
& ( ( B @ as_input @ ( B @ halts2 ) )
=> ~ ( B @ as_input @ ( A @ halts2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(36,plain,
( ? [A: program] :
! [B: program] :
( ( ~ ( B @ as_input @ ( B @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) )
& ( ( B @ as_input @ ( B @ halts2 ) )
=> ( ( good @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ~ ( B @ as_input @ ( B @ halts2 ) )
=> ( ( bad @ ( A @ outputs ) )
& ( B @ as_input @ ( A @ halts2 ) ) ) )
& ( ( B @ as_input @ ( B @ halts2 ) )
=> ~ ( B @ as_input @ ( A @ halts2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[10,21,12,7,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003_1 : TPTP v9.3.1. Released v5.0.0.
% 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
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 23:19:24 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 1.31/1.19 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.71/1.50 % [INFO] Parsing done (297ms).
% 1.94/1.52 % [INFO] Running in sequential loop mode.
% 2.84/2.08 % [INFO] eprover registered as external prover.
% 2.84/2.09 % [INFO] Scanning for conjecture ...
% 3.06/2.19 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.18/2.23 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.18/2.26 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.18/2.27 % [INFO] Type checking passed.
% 3.18/2.27 % [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 ...
% 5.06/3.07 % External prover 'e' found a proof!
% 5.06/3.07 % [INFO] Killing All external provers ...
% 5.06/3.07 % Time passed: 2466ms (effective reasoning time: 1538ms)
% 5.06/3.07 % 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)>
% 5.06/3.07 % Axioms used in derivation (4): p1, p3, p2, p4
% 5.06/3.07 % No. of inferences in proof: 12
% 5.06/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2466 ms resp. 1538 ms w/o parsing
% 5.06/3.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.06/3.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------