TSTP Solution File: GRP017-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP017-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 11:13:00 EDT 2023
% Result : Unsatisfiable 2.69s 1.60s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 34 ( 21 unt; 7 typ; 0 def)
% Number of atoms : 43 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 156 ( 18 ~; 16 |; 0 &; 122 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(identity_type,type,
identity: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(a_type,type,
a: $i ).
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(25,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(1,negated_conjecture,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_c) ).
thf(14,plain,
b != c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(21,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] : ( product @ A @ identity @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(18,plain,
! [A: $i] : ( product @ A @ identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
product @ a @ c @ identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_identity) ).
thf(31,plain,
product @ a @ c @ identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(20,plain,
! [A: $i] : ( product @ A @ ( inverse @ A ) @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
product @ a @ b @ identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_identity) ).
thf(29,plain,
product @ a @ b @ identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
product @ c @ a @ identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_a_is_identity) ).
thf(32,plain,
product @ c @ a @ identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2,axiom,
! [A: $i] : ( product @ identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(17,plain,
! [A: $i] : ( product @ identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(22,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(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(27,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(11,axiom,
product @ b @ a @ identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_is_identity) ).
thf(30,plain,
product @ b @ a @ identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(19,plain,
! [A: $i] : ( product @ ( inverse @ A ) @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[25,14,21,18,31,20,29,32,17,22,27,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP017-1 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.14 % Command : run_Leo-III %s %d
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 19 01:43:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.93/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (112ms).
% 1.22/0.96 % [INFO] Running in sequential loop mode.
% 1.66/1.17 % [INFO] eprover registered as external prover.
% 1.76/1.18 % [INFO] cvc4 registered as external prover.
% 1.76/1.18 % [INFO] Scanning for conjecture ...
% 1.76/1.23 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.90/1.25 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.95/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.95/1.26 % [INFO] Type checking passed.
% 1.95/1.27 % [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 ...
% 2.69/1.60 % External prover 'e' found a proof!
% 2.69/1.60 % [INFO] Killing All external provers ...
% 2.69/1.60 % Time passed: 1090ms (effective reasoning time: 638ms)
% 2.69/1.60 % 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)>
% 2.69/1.60 % Axioms used in derivation (12): total_function1, b_times_a_is_identity, left_identity, left_inverse, right_inverse, associativity1, c_times_a_is_identity, a_times_b_is_identity, total_function2, associativity2, a_times_c_is_identity, right_identity
% 2.69/1.60 % No. of inferences in proof: 27
% 2.69/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1090 ms resp. 638 ms w/o parsing
% 2.69/1.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.69/1.64 % [INFO] Killing All external provers ...
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