TSTP Solution File: SET672^3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET672^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 : Tue May 21 03:03:30 EDT 2024
% Result : Theorem 3.13s 2.03s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 3 unt; 2 typ; 2 def)
% Number of atoms : 11 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 2 ~; 0 |; 5 &; 32 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-4 aty)
% Number of variables : 25 ( 7 ^ 18 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_rel_on_type,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(is_rel_on_def,definition,
( is_rel_on
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
! [D: $i,E: $i] :
( ( A @ D @ E )
=> ( ( B @ D )
& ( C @ E ) ) ) ) ) ).
thf(restrict_rel_codomain_type,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(restrict_rel_codomain_def,definition,
( restrict_rel_codomain
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i,D: $i] :
( ( B @ D )
& ( A @ C @ D ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( is_rel_on @ B @ C @ D )
=> ( is_rel_on @ ( restrict_rel_codomain @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( is_rel_on @ B @ C @ D )
=> ( is_rel_on @ ( restrict_rel_codomain @ B @ A ) @ C @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ! [E: $i,F: $i] :
( ( B @ E @ F )
=> ( ( C @ E )
& ( D @ F ) ) )
=> ! [E: $i,F: $i] :
( ( ( A @ F )
& ( B @ E @ F ) )
=> ( ( C @ E )
& ( A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET672^3 : TPTP v8.2.0. Released v3.6.0.
% 0.00/0.11 % Command : run_Leo-III %s %d
% 0.10/0.30 % Computer : n028.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon May 20 12:16:09 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.92/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.09 % [INFO] Parsing done (201ms).
% 1.47/1.10 % [INFO] Running in sequential loop mode.
% 1.89/1.45 % [INFO] eprover registered as external prover.
% 1.89/1.45 % [INFO] cvc4 registered as external prover.
% 1.89/1.46 % [INFO] Scanning for conjecture ...
% 2.40/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.40/1.64 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.40/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.40/1.64 % [INFO] Type checking passed.
% 2.40/1.65 % [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 ...
% 3.13/2.03 % External prover 'e' found a proof!
% 3.13/2.03 % [INFO] Killing All external provers ...
% 3.13/2.03 % Time passed: 1601ms (effective reasoning time: 926ms)
% 3.13/2.03 % 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)>
% 3.13/2.03 % Axioms used in derivation (0):
% 3.13/2.03 % No. of inferences in proof: 4
% 3.13/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1601 ms resp. 926 ms w/o parsing
% 3.53/2.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.53/2.12 % [INFO] Killing All external provers ...
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