%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% 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 6.37s 3.32s
% Output : Refutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 0 equ; 0 cnn)
% Maximal formula atoms : 19 ( 8 avg)
% Number of connectives : 232 ( 11 ~; 0 |; 45 &; 149 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 41 ( 0 ^; 32 !; 9 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(algorithm_decl,type,
algorithm: $i > $o ).
thf(program_decl,type,
program: $i > $o ).
thf(decides_decl,type,
decides: $i > $i > $i > $o ).
thf(halts2_decl,type,
halts2: $i > $i > $o ).
thf(halts3_decl,type,
halts3: $i > $i > $i > $o ).
thf(outputs_decl,type,
outputs: $i > $i > $o ).
thf(good_decl,type,
good: $i ).
thf(bad_decl,type,
bad: $i ).
thf(1,conjecture,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ algorithm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ algorithm ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ~ ? [A: $i] :
( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ algorithm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
( ? [A: $i] :
( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ algorithm ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ program ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(11,plain,
( ? [A: $i] :
( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ algorithm ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ program ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ program ) )
=> ! [B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ halts2 ) )
& ( B @ program ) )
=> ( ( bad @ ( A @ outputs ) )
& ( C @ ( B @ ( A @ halts3 ) ) ) ) )
& ( ( ( C @ ( B @ halts2 ) )
& ( B @ program ) )
=> ( ( good @ ( A @ outputs ) )
& ( C @ ( B @ ( A @ halts3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(17,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ program )
=> ! [C: $i] : ( C @ ( B @ ( A @ decides ) ) ) )
& ( A @ program ) )
=> ! [B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ halts2 ) )
& ( B @ program ) )
=> ( ( bad @ ( A @ outputs ) )
& ( C @ ( B @ ( A @ halts3 ) ) ) ) )
& ( ( ( C @ ( B @ halts2 ) )
& ( B @ program ) )
=> ( ( good @ ( A @ outputs ) )
& ( C @ ( B @ ( A @ halts3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ halts2 ) )
& ( B @ program ) )
=> ( ( bad @ ( A @ outputs ) )
& ( C @ ( B @ ( A @ halts3 ) ) ) ) )
& ( ( ( C @ ( B @ halts2 ) )
& ( B @ program ) )
=> ( ( good @ ( A @ outputs ) )
& ( C @ ( B @ ( A @ halts3 ) ) ) ) ) )
& ( A @ program ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( ( bad @ ( A @ outputs ) )
& ( C @ ( C @ ( A @ halts3 ) ) )
& ( C @ program ) )
=> ( ( bad @ ( B @ outputs ) )
& ( C @ ( B @ halts2 ) ) ) )
& ( ( ( good @ ( A @ outputs ) )
& ( C @ ( C @ ( A @ halts3 ) ) )
& ( C @ program ) )
=> ~ ( C @ ( B @ halts2 ) ) ) )
& ( B @ program ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(28,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ halts2 ) )
& ( B @ program ) )
=> ( ( bad @ ( A @ outputs ) )
& ( C @ ( B @ ( A @ halts3 ) ) ) ) )
& ( ( ( C @ ( B @ halts2 ) )
& ( B @ program ) )
=> ( ( good @ ( A @ outputs ) )
& ( C @ ( B @ ( A @ halts3 ) ) ) ) ) )
& ( A @ program ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( ( bad @ ( A @ outputs ) )
& ( C @ ( C @ ( A @ halts3 ) ) )
& ( C @ program ) )
=> ( ( bad @ ( B @ outputs ) )
& ( C @ ( B @ halts2 ) ) ) )
& ( ( ( good @ ( A @ outputs ) )
& ( C @ ( C @ ( A @ halts3 ) ) )
& ( C @ program ) )
=> ~ ( C @ ( B @ halts2 ) ) ) )
& ( B @ program ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(128,plain,
$false,
inference(e,[status(thm)],[6,11,17,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.15/0.40 % Computer : n004.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 23:19:09 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 1.32/1.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.56 % [INFO] Parsing done (287ms).
% 1.85/1.58 % [INFO] Running in sequential loop mode.
% 2.54/2.01 % [INFO] eprover registered as external prover.
% 2.54/2.02 % [INFO] Scanning for conjecture ...
% 2.79/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.98/2.15 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.98/2.18 % [INFO] Problem is first-order (TPTP FOF).
% 2.98/2.19 % [INFO] Type checking passed.
% 2.98/2.19 % [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 ...
% 6.37/3.32 % External prover 'e' found a proof!
% 6.37/3.32 % [INFO] Killing All external provers ...
% 6.37/3.32 % Time passed: 2700ms (effective reasoning time: 1729ms)
% 6.37/3.32 % 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)>
% 6.37/3.32 % Axioms used in derivation (3): p1, p2, p3
% 6.37/3.32 % No. of inferences in proof: 10
% 6.37/3.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2700 ms resp. 1729 ms w/o parsing
% 6.37/3.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.37/3.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------