TSTP Solution File: COM003_1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 04:56:17 EDT 2024
% Result : Theorem 2.87s 1.51s
% Output : Refutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 24 ( 4 unt; 12 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 : 12 ( 12 >; 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_type,type,
bad: output ).
thf(good_type,type,
good: output ).
thf(decides_type,type,
decides: algorithm > program > input > $o ).
thf(halts2_type,type,
halts2: program > input > $o ).
thf(halts3_type,type,
halts3: program > program > input > $o ).
thf(outputs_type,type,
outputs: program > output > $o ).
thf(algorithm_of_type,type,
algorithm_of: program > algorithm ).
thf(as_input_type,type,
as_input: program > input ).
thf(3,axiom,
( ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C )
=> ? [A: program] :
! [B: program,C: input] : ( decides @ ( algorithm_of @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(10,plain,
( ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C )
=> ? [A: program] :
! [B: program,C: input] : ( decides @ ( algorithm_of @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
( ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
thf(20,plain,
( ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
( ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ~ ( halts2 @ A @ ( as_input @ B ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
thf(34,plain,
( ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ~ ( halts2 @ A @ ( as_input @ B ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: program,B: program,C: input] :
( ( decides @ ( algorithm_of @ A ) @ B @ C )
=> ! [D: program,E: input] :
( ( ( halts2 @ D @ E )
=> ( ( halts3 @ A @ D @ E )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ D @ E )
=> ( ( halts3 @ A @ D @ E )
& ( outputs @ A @ bad ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
thf(12,plain,
! [A: program,B: program,C: input] :
( ( decides @ ( algorithm_of @ A ) @ B @ C )
=> ! [D: program,E: input] :
( ( ( halts2 @ D @ E )
=> ( ( halts3 @ A @ D @ E )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ D @ E )
=> ( ( halts3 @ A @ D @ E )
& ( outputs @ A @ bad ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
~ ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
~ ~ ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ~ ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
$false,
inference(e,[status(thm)],[10,20,34,12,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.09/0.27 % Computer : n017.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Fri Jun 21 00:14:40 EDT 2024
% 0.09/0.27 % CPUTime :
% 0.81/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.01/0.83 % [INFO] Parsing done (113ms).
% 1.01/0.84 % [INFO] Running in sequential loop mode.
% 1.47/1.04 % [INFO] eprover registered as external prover.
% 1.47/1.04 % [INFO] Scanning for conjecture ...
% 1.65/1.10 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.65/1.12 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.65/1.14 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.65/1.15 % [INFO] Type checking passed.
% 1.65/1.15 % [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 ...
% 2.87/1.51 % External prover 'e' found a proof!
% 2.87/1.51 % [INFO] Killing All external provers ...
% 2.87/1.51 % Time passed: 1071ms (effective reasoning time: 667ms)
% 2.87/1.51 % 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)>
% 2.87/1.51 % Axioms used in derivation (4): p1, p3, p4, p2
% 2.87/1.51 % No. of inferences in proof: 12
% 2.87/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1071 ms resp. 667 ms w/o parsing
% 2.97/1.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.97/1.54 % [INFO] Killing All external provers ...
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