TSTP Solution File: GRP022-1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : GRP022-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 7 07:43:04 EDT 2024
% Result : Unsatisfiable 2.68s 1.69s
% Output : Refutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 24 ( 13 unt; 5 typ; 0 def)
% Number of atoms : 35 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 136 ( 18 ~; 16 |; 0 &; 102 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 0 ^ 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(inverse_type,type,
inverse: $i > $i ).
thf(a_type,type,
a: $i ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(identity_type,type,
identity: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(1,negated_conjecture,
( ( inverse @ ( inverse @ a ) )
!= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_inverse_is_original) ).
thf(10,plain,
( ( inverse @ ( inverse @ a ) )
!= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [A: $i] : ( product @ A @ identity @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(14,plain,
! [A: $i] : ( product @ A @ identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(21,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)],[8]) ).
thf(2,axiom,
! [A: $i] : ( product @ identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(13,plain,
! [A: $i] : ( product @ identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(17,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(16,plain,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',associativity2) ).
thf(23,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)],[9]) ).
thf(4,axiom,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(15,plain,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[10,14,21,13,17,18,16,23,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : GRP022-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n007.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 16:04:39 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.12/0.99 % [INFO] Parsing done (112ms).
% 1.12/0.99 % [INFO] Running in sequential loop mode.
% 1.73/1.24 % [INFO] eprover registered as external prover.
% 1.77/1.24 % [INFO] cvc4 registered as external prover.
% 1.77/1.24 % [INFO] Scanning for conjecture ...
% 1.77/1.29 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.77/1.31 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.99/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/1.32 % [INFO] Type checking passed.
% 1.99/1.33 % [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 ...
% 2.68/1.68 % External prover 'e' found a proof!
% 2.68/1.68 % [INFO] Killing All external provers ...
% 2.68/1.68 % Time passed: 1149ms (effective reasoning time: 686ms)
% 2.68/1.68 % 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)>
% 2.68/1.68 % Axioms used in derivation (8): total_function1, left_identity, left_inverse, right_identity, right_inverse, associativity1, total_function2, associativity2
% 2.68/1.68 % No. of inferences in proof: 19
% 2.68/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1149 ms resp. 686 ms w/o parsing
% 2.96/1.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.96/1.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------