TSTP Solution File: GRP004-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 : Fri May 19 11:12:59 EDT 2023
% Result : Unsatisfiable 2.69s 1.58s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 15 ( 7 unt; 4 typ; 0 def)
% Number of atoms : 23 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 94 ( 14 ~; 12 |; 0 &; 68 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(identity_type,type,
identity: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(4,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(10,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( product @ a @ A @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_inverse) ).
thf(6,plain,
! [A: $i] :
~ ( product @ a @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [A: $i] : ( product @ identity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(9,plain,
! [A: $i] : ( product @ identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(12,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(8,plain,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
$false,
inference(e,[status(thm)],[10,6,9,12,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n024.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 01:41:23 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/0.99 % [INFO] Parsing done (110ms).
% 1.29/1.00 % [INFO] Running in sequential loop mode.
% 1.62/1.20 % [INFO] eprover registered as external prover.
% 1.62/1.21 % [INFO] cvc4 registered as external prover.
% 1.62/1.21 % [INFO] Scanning for conjecture ...
% 1.82/1.26 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.89/1.28 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.89/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 1.89/1.29 % [INFO] Type checking passed.
% 1.89/1.29 % [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 ...
% 2.69/1.58 % External prover 'e' found a proof!
% 2.69/1.58 % [INFO] Killing All external provers ...
% 2.69/1.58 % Time passed: 1039ms (effective reasoning time: 579ms)
% 2.69/1.58 % 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)>
% 2.69/1.58 % Axioms used in derivation (4): associativity1, left_identity, associativity2, left_inverse
% 2.69/1.58 % No. of inferences in proof: 11
% 2.69/1.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1039 ms resp. 579 ms w/o parsing
% 2.69/1.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.69/1.60 % [INFO] Killing All external provers ...
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